Pg 1 Solve each word problem 1. Marie rode her bicycle from her home to the bicycle shope in town and then walked back home. If she averaged 6 miles per hour riding and 3 miles per hour walking, how far is it from her home to the bicycle shop if her total travel time was 1 hour? 2. A ski lift carries a skier up a slope at the rate of 800 feet per minute and he returns from the top to the bottom on a path parallel to the lift at an average rate of 2640 feet per minute. How long is the lift if the round trip traveling time is 20 minutes? 3. A hiker climbs a mountain path at the rate of 2 miles per hour. Following the same path down the mountain, the hiker has a rate of 4 miles per hour. If the round trip took 3 hours, how far is it from the top to the bottom of the mountain? 4. A man leaves the town of Elmsville at 8:00 am and drives to Oak City at a constant rate of 50 miles per hour. Two hours later, a woman leaves Elmsville following the same route to Oak City. The man and woman arrive in Oak City at 3:00 pm. What was the rate of the woman? How far is Elmsville from Oak City? 5. Tim and a friend left a campsite on a trip down a river in a canoe, maintaining a constant speed of 4 miles per hour. Four hours later, Tim s father set out after them in a motorboat carrying the camping supplies. The motorboat traveled at a rate of 12 miles per hour. How long after he started did Tim s father overtake the boys? 6. It takes a passenger train 2 hours less time than it takes a freight train to make the trip from Brownsville to Greentown. If the passenger train averages 60 miles per hour on the trip while the freight train averages 40 miles per hour on the trip, how far is it from Brownsville to Greentown? Answers: 1. 2 miles 2. 13,200 feet 3. 4 miles 4. 70 miles per hour; 350 miles 5. 2 hours 6. 240 miles
Pg 2 (1) When the smaller of two even consecutive integers is added to 3 times the larger, the result is 230. Find the smaller integer. (2) When the smaller of two even consecutive integers is added to 4 times the larger, the result is 218. Find the smaller integer. (3) If 2 times the smaller of two consecutive integers is added to 6 times the larger, the result is 150 Find the smaller integer. (4) If 1 times the smaller of two consecutive integers is added to 3 times the larger, the result is 39. Find the smaller integer. (5) The smallest of the three consecutive integers is added to twice the largest, producing a result 20 less than four times the middle integer. Find the smallest integer. (6) The smallest of the three consecutive integers is added to twice the largest, producing a result 5 less than four times the middle integer. Find the smallest integer. (7) A man has $ 0.70 in dimes and nickels. He has 8 coins altogether. How many nickels does she have? (8) A man has $ 0.55 in dimes and nickels. He has 6 coins altogether. How many nickels does she have? (9) A woman has $ 0.85 in dimes and nickels. She has 4 more dimes than nickels. How many nickels does she have? (10) A woman has $ 1.90 in dimes and nickels; she has 4 more dimes than nickels. How many nickels does she have? (11) A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 4 less of the fives. The total value of the money is $280.00. (12) A bank teller has some five-dollar bills and some twenty-dollar bills. the teller has 4 less of the fives. The total value of the money is $480.00.
Pg 3 (13) A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has a total of 24 bills. The total value of the money is $330.00. (14) A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has a total of 32 bills. The total value of the money is $430.00. (15) A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 4 more of the twenties. The total value of the money is $305.00. (16) A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 4 more of the twenties. The total value of the money is $505.00. (17) Caroline needs a 3 % solution. How many liters of a 1 % solution should she add to 2 liters of a 32 % solution to get a 3 % solution? (18) Caroline needs a 7 % solution. How many liters of a 1 % solution should she add to 18 liters of a 29 % solution to get a 7 % solution? (19) How many gallons of pure alcohol solution should be added to 63 gal of a 32 % alcohol solution to make a 37 % solution? (20) How many gallons of pure alcohol solution should be added to 12 gal of a 12 % alcohol solution to make a 34 % solution? (21) How many gallons of 16 % alcohol solution should be added to 30 gal of a 45 % alcohol solution to make a 21 % solution? (22) How many gallons of 13 % alcohol solution should be added to 20 gal of a 43 % alcohol solution to make a 23 % solution? (23) How many gallons of 51 % alcohol solution should be added to some of a 57 % alcohol solution to make a 438 gal of a 55 % solution? (24) How many gallons of 16 % alcohol solution should be added to some of a 78 % alcohol solution to make a 576 gal of a 16 % solution? (25) Marion wants to dilute 2 gal of a 28 % soap solution to make a 8 % solution. How much pure water should she add to make the 8 % solution?
Pg 4 (26) Marion wants to dilute 2 gal of a 14 % soap solution to make an 7 % solution. How much pure water should she add to make the 7% solution? (27) Mary and David are 833 miles apart and are heading toward each other to meet for dinner. Mary is traveling at 54 mph and David is traveling at 65 mph. how longs before they meet? (28) Mary and David are 1240 miles apart and are heading toward each other to meet for dinner. Mary is traveling at 51 mph and David is traveling at 73 mph. How longs before they meet? (29) David and Caroline leave buoy 15 traveling in opposite directions. If David travels at 66 mph and Mary travels at 52 mph, then how long will it be before they are 1180 miles apart? (30) David and Caroline leave buoy 15 traveling in opposite directions. If David travels at 66 mph and Mary travels at 77 mph, then how long will it be before they are 572 miles apart? (31) Fred leaves John's house and drives toward Tampa at 27 mph. Kim leaves 2 hours later and drives the same route at 45 mph. How long will it take Kim to overtake Fred? (32) Fred leaves john's house and drives toward Tampa at 21 mph. Kim leaves 3 hours later and drives the same route at 42 mph. How long will it take Kim to overtake Fred?
pg 5 1. A car left an intersection and traveled east at 32 mph. Another car left the same intersection at the same time and traveled west at 48 mph. How long will it take before the cars are 160 miles apart? 2. A train left Orlando, FL at the same time another train left Atlanta GA. The trains traveled towards each other. The rate of the Orlando train was 12 miles per hour faster than the Atlanta train. In 4 hours the trains passed each other. If the distance between Orlando and Atlanta is 408 miles, find the rate of each train. 3. Heidi and Angela started biking at the same time on opposite ends of a 53 mile trail. The rate that Heidi rode her bike exceeded the rate that Angela rode her bike by 4 mph. At the end of 2 hours, they were still 5 miles apart. Find the rate of each person. 4. A bus entered the Interstate and traveled at a constant speed of 40 mph. Two hours later a second bus followed the first bus, entering the Interstate from the same point as the first bus, and traveled at a constant speed of 60 mph. How long will it take the second bus to catch up with the first bus? 5. John drove his car down a mountain road at an average rate of 30 mph and returned over the same road at an average rate of 20 mph. If his trip took 5 hours, how far did he drive down the road before he turned around and drove back? 1. One car traveling at 30 mph and another car traveling at 40 mph left from the same place at the same time and traveled in opposite directions. How long will it take before the cars are 630 miles apart? 2. Two people started from the same point at the same time and traveled in opposite directions. One traveled at 60 mph and the other at 50 mph. How long will it take before the two people are 440 miles apart? 3. Two jets took off from an airport at the same time using parallel runways. One flew east at 220 mph and the other flew west at 450 mph. How long will it take before the planes are 2010 miles apart? 4. Two trucks started traveling from the same place at 9:00 A.M. One truck traveled north going 45 mph and the other traveled south going 50 mph. What time will it be when the trucks are 380 miles apart? 5. Two trains began their trip from the same station at 8:00 A.M. One train traveled north at the rate of 44 mph and the other traveled south at the rate of 46 mph. What time will it be when the trains are 390 miles apart? 6. An airplane left Miami at the same time another left Santiago, Chile. The two planes flew toward each other at rates of 625 mph and 575 mph. If Miami and Santiago are 4200 miles apart, how long will it take until the planes pass each other? 7. Miami and Orlando are 210 miles apart. A truck traveled from Miami toward Orlando at the rate of 48 mph. Another truck traveled from Orlando toward Miami at the rate of 42 mph. Both trucks started traveling at the same time. How many miles did each travel before they met? 8. At 11 A.M. two trucks start traveling toward each other at average rates of 45 and 53 mph. At the beginning of their trip they were 588 miles apart. What time will it be when they pass each other? 9. Two train stations are 1000 miles apart. Two trains leave each of these stations at the same time and travel toward each other. One of the trains averages 63 mph and the other averages 57 mph. How long will it take until they pass each other?
Pg 6 10. Two planes started at the same time from the same airport and flew in opposite directions. One of the planes flew 70 miles per hour faster than the other. In 5 hours, the planes were 3850 miles apart. Find the rate of each plane. 11. Two buses started from the same depot at the same time and traveled in opposite directions. After traveling 4 hours, they were 480 miles apart. The rate of the fast bus exceeded the rate of the slow bus by 10 mph. Find the rate of each bus. 12. Two trains started from the same place at the same time and traveled in opposite directions. One train s speed was 8 mph faster than the other. In 6 hours, they were 552 miles apart. Find the rate of each train. 13. Two planes left at the same time from two airports that are 3600 miles apart and flew toward each other. One of planes flew twice the speed of the other. In 4 hours, they passed each other. Find the rate of each plane. 14. Two cars started from the same place and 9:00 A.M. and traveled in opposite directions. When it was 12:30 P.M. the two cars were 252 miles apart. The rate of the fast car exceeded the rate of the slow car by 8 mph. Find the rate of each car. 15. A family on vacation made a trip of 350 miles by boat and by train. They traveled 2 hours by boat and 4 hours by train. If the train averaged 20 mph more than the boat, find the rate of both the boat and the train. 16. It took an airplane 7 hours to fly 4075 miles. During the first 3 hours of the flight it had good weather. It then ran into bad weather, which decreased its rate by 75 mph for the rest of the flight. Find the rate on each part of the flight. 17. Two planes started at the same time from two airports which are 2300 miles apart and flew toward each other. One plane flew 310 mph, and the other flew 390 mph. In how many hours were the planes still 200 miles apart? 18. Two trains started toward each other from stations which were 260 miles apart at rates of 22 and 28 mph. They began their trip at 5:00 P.M. At what time were the trains still 60 miles apart? 19. Two cars started from the same town and traveled east on the same road. They began their journey at 7:00 A.M. One car averaged 41 mph, and the other car averaged 55 mph. In how many hours were the cars 84 miles apart? 20. At 10 A.M. Joyce left the shopping center driving her car at the rate of 30 mph. At 11 A.M. her brother Howie left the same shopping center, going the same direction as Joyce on the same road. He drove at the rate of 40 mph. In how many hours will Howie pass Joyce? 21. At 4 P.M. a plane took off from an airport and flew east at 300 mph. At 4:30 P.M. another plane left the same airport, flying east at 350 mph. At what time did the second plane pass the first plane? 22. David took a 5 hour hike. He walked one way at the rate of 2 mph and returned on the same road at the rate of 3 mph. How far did he walk before he turned around and walked back? 23. A hurricane plane made a round trip investigation flight. The flight took a total of 10 hours. The pilot flew into the hurricane area at a rate of 360 mph and returned over the same route at a rate of 240 mph. How many miles did the plane fly before it turned back?
pg 7 1. The first painter can finish a paint job in 2 hours. The second painter can finish the same job in 2 hours. How long would it take them to finish the job if they are working together. You can give the answer as a fraction m/n. 2. Two gardners can finish a plowing job in 2 hours. The first gardner, working alone, can finish the same job in 8 hours. How long would it take the the second gardner to finish the same job alone. You can give the 3. Three workers are to accomplish a job. The first worker can finish the job in 6 hours. The second worker can finish the job in 2 hours. The third worker can finish the job in 5 hours. How long would it take the three workers to finish the job if they work together? You can give the 4. Three workers are to accomplish a job. The first worker can finish the job in 7 hours. The second worker can finish the job in 6 hours. The third worker can finish the job in x hours. The three workers can finish the job in 2 hours if they work together. Find x. You can give the 5. A pool has two inlet pipes. The first inlet can fill the pool in 6 hours, the other can fill it in 8 hours. If the first pipe is open for 5 hours and then the second is open. How long will take for the pool to be filled after the second pipe is open. You can give your 6. A pond has an inlet to fill it up and an outlet to drain it. The inlet can fill it in 3 hours and the the outlet can drain it in 11 hours. Suppose the pond was empty and the person in charge of filling it up opened the inlet but forget to close the outlet. How long will take for the pond to get filled? You can give your answer as a fraction m/n. 7. A pond has an inlet to fill it up and an outlet to drain it. The inlet can fill it in 3 hours and the the outlet can drain it in 9 hours. Suppose the pond was empty and the person in charge of filling it up opened the inlet but forgot to close the outlet. After 2 hours, he realized that the outlet is still open. At that time, he closed the outlet. How long did it take for the pond to get filled after the outlet was closed? You can give your 8. Two gardners can finish a plowing job in 4 hours. The first gardner, working alone, can finish the same job in 5 hours. How long would it take the the second gardner to finish the same job alone. You can give the 9. Three workers are to accomplish a job. The first worker can finish the job in 7 hours. The second worker can finish the job in 6 hours. The third worker can finish the job in x hours. The three workers can finish the job in 3 hours if they work together. Find x. You can give the 10. A pool has two inlet pipes. The first inlet can fill the pool in 6 hours, the other can fill it in 5 hours. If the first pipe is open for 4 hours and then the second is open. How long will take for the pool to be filled after the second pipe is open. You can give your 11. A pond has an inlet to fill it up and an outlet to drain it. The inlet can fill it in 2 hours and the the outlet can drain it in 5 hours. Suppose the pond was empty and the person in charge of filling it up opened the inlet but forget to close the outlet. How long will take for the pond to get filled? You can give your answer as a fraction m/n. 12. A pond has an inlet to fill it up and an outlet to drain it. The inlet can fill it in 4 hours and the the outlet can drain it in 5 hours. Suppose the pond was empty and the person in charge of filling it up opened the inlet but forgot to close the outlet. After 3 hours, he realized that the outlet is still open. At that time, he closed the outlet. How long did it take for the pond to get filled after the outlet was closed? You can give your