Uniform Motion Problems Of Equal Distances Example 1 On Tuesday, the express train made the trip in 12 hours. On Wednesday, the freight train made the same trip in 16 hours. Find the rate of each train if the rate of the freight train was 15 kph less than the rate of the express train. Example 2 The members of the girls club hiked to Lake Tenkiller at 2 mph. Mr. Ali gave them a ride back home at 12 mph. Find their hiking time if it was 5 hours longer than their riding time. How far was it to Lake Tenkiller? Example 3 Durant drove to the oasis in 2 hours and Madill walked to the oasis in 10 hours. How far is it to the oasis if Durant drove 16 mph faster than Madill walked? Example 4 Candide and Pangloss walked to the site of the disaster in 9 hours. The next morning they jogged back home in 3 hrs. How far did they jog if they jogged 4 mph faster than they walked? Example 5 On Monday, Voltaire drove to town at 60 mph. On Tuesday he drove to town at 40 mph. If the total traveling time for both trips was 15 hours, how far was it to town? Example 6 In the morning the passenger train made the trip in 3 hours. In the afternoon the freight train mad the same trip in 7 hours. Find the rate of each if the rate of the freight train was 40 mph less than the rate of the passenger train. Example 7 Vanessa rode her bike to the conclave at 10 kph and then walked back to school at 4 kph. If the round trip took her 14 hours, how far was it to the site of the conclave?
Example 8 Norma and david crawled to the barn and then hopped back to the house. They crawled at 300 cm per minute and hopped at 400 cm per minute. If the round trip took 7 minutes, how long did they crawl? How far was it to the barn? Example 9 Annette drove to Shawnee in 4 hours and drove back in 3 hours. What were her speeds if her speed coming back was 11 mph greater than her speed going? Example 10 At noon Joyce drove drove to the lake at 30 mph, but she made the long walk back home at 4 mph. How long did she walk if she was gone for 17 hours? How far did she walk? Example 11 Gaskin and Sloan raced to the cotton patch. Gaskin s speed was 12 kph, while Sloan s was only 8 kph. What was the time of each if Gaskin s time was 5 hrs less than Sloan s time? Example 12 Alphasia headed for the rodeo at 9 A.M. at 30 mph. At 11 A.M. Bubba headed after her at 60 mph. What time was it when Bubba caught Alphasia? Example 13 Billy ran to town at 8 kph and then walked back home at 3 kph. How far was it to town if the round trip took 11 hours? Example 14 Wendy drove at 60 mph. Thus, she made the trip in 1 hour less than it took Deborah because Deborah only drove at 50 mph. How long did each of them drive and how long was the trip? Example 15 It took Theseus 60 hours to get there with black sails and 100 hours to come back with white sails. How far was it if his speed with black sails was 2 mph greater than his speed with white sails?
Example 16 Willy drove to Castle Rock at 40 mph and returned walking 4 mph. Find his walking time if it was 9 hours longer than his driving time. How far was it to Castle Rock? Example 17 Robert ran to the redoubt while Wilbur walked to the parapet. Both distances were the same, but Robert s speed was 6 mph while Wilbur s speed was 8 mph. What was the time of each if Robert s time was 2 hours longer than Wilbur s? Example 18 Josephine walked to Brundig and then trotted back home. She walked at 2 mph and trotted at 4 mph. How far was it to Brundig if her walking time was 2 hours longer than her trotting time? Example 19 Milton ran north at 8 kph. Four hours later Harriet set out in pursuit at 16 kph. How long did it take Harriet to catch Milton? Example 20 The train made the trip in 4 hours. The girls walked it in 48 hours. How far was it if the speed of the train was 55 mph faster than the girls walked? Example 21 Louis ran to Versailles and then walked back to town. His running rate was 6 kph and his walking rate was 3 kph. How far was it to Versailles if the round trip took 6 hours? Example 22 The sciolist headed for town at 30 mph. Two hours later, the charlatan began his pursuit at 50 mph. How long did it take the charlatan to catch the sciolist? Example 23 Birthe rode to town in the bus at 20 mph. Then she trotted back home at 8 mph. If her total traveling time was 14 hours, how far was it to town?
Example 24 The doyenne walked to the meeting at 2 mph and caught a ride home in an old truck at 10 mph. How far was it to the meeting place if her total traveling time was 18 hours? Example 25 The track team ran to the cemetery at 8 mph and trotted back home at 6 mph. If the total trip took 7 hours, how far was it to the cemetery? Example 26 Wanatobe walked to the moot at 4 mph then rode back in a bus at 24 mph. If her total traveling time was 14 hours, how far was it to the moot? Example 27 Judy walked into the city at 5 kph and then rode a bus back home at 30 kph. It was a long trip - she spent 21 hours traveling. How far did she walk? Example 28 Howell hopped to the hostel at 5 mph and hobbled back to the helicopter at 2 mph. How far was it to the hostel if the round trip too 28 hours? Example 29 Rosie ran to the park at 7 mph and walked back home at 3 mph. How far was it to the park if the round trip took 20 hours? Example 30 Hannibal rode the elephant to the outskirts of Rome at 2 kph and then took a chariot back to camp at 10 kph. If the total trip took 18 hours, how far was it from camp to the outskirts of Rome? Example 31 The express train made the trip in 20 hours. The freight train took 25 hours because it was 10 mph slower than the express train. What was the speed of each train? Example 32 Paula ran to Hugo in 6 hours, while Busking walked the same distance in 72 hours. How fast did Paula run if her speed was 11 kph faster than Busking s? How far was it to Hugo?
Uniform Motion Problems Using The Sum Of Distances Example 33 A southbound bus left Fort Walton Beach at 9 A.M. Two hours later a northbound bus left the same station. If the buses traveled at the same rate and were 352 km apart at 2 P.M., find the rate of the buses. Example 34 A train starts from Toledo at 11 A.M. and heads for Makinaw, 332 km away. At the same time, a train leaves Makinaw and heads for Toledo at 65 kph. If the trains meet at 1 P.M., what is the rate of the first train? Example 35 The ships were 400 miles apart at midnight and were headed directly toward each other. If they collided at 8 A.M., find the speed of both ships if one was 20 mph faster than the other. Example 36 An eastbound bust left Ukiah at noon. Two hours later a westbound bus left the same station. If the buses traveled at the same rate and were 500 km apart at 6 P.M., find the rate of each bus. Example 37 A train starts from Peoria at 2 P.M. and heads for Reedley, 750 km away. At the same time a train leaves Reedley and heads for Peoria at 85 kph. If the trains meet at 5 P.M., what is the rate of the first train? Example 38 Two ships were 700 mi apart at midnight and were headed directly toward each other. If they collided at 10 A.M., find the speeds of both ships if one was traveling 30 mph faster than the other. Example 39 The cars were 300 mi apart at noon and were headed directly toward each other. If they collided at 3 P.M., find the speeds of both cars if one was traveling 10 mph faster than the other. Example 40 At 3 P.M., Brunhilde headed north at 30 kph. Two hours later Ludwig headed south at 40 kph. At what time will they be 340 km apart?
Example 41 At noon, Sarah headed from Elk City to Idabel at 60 mph. Two hours later Joan headed from Idabel to Elk City at 46 mph. If it is 332 mi from Elk City to Idabel, what time did they meet? Example 42 Ed and Alice walked to the dock at 5 mph, jumped into the boat, and motored to Destin at 15 mph. If the total distance was 20 mi and the trip took 2 hours in all, how far did they go by boat? Example 43 At noon the armadillo left the wild kingdom and headed north at 3 kph. Two hours later the raccoon left the same kingdom and headed south at 5 kph. At what time will the animals be 38 km apart? Example 44 Frederick headed for Lutzen at 3 kph. Later he increased his speed to 4 kph. If it was 52 km to Lutzen and the total time of travel was 15 hours, how long did he travel at 3 kph? Example 45 The passenger train headed north at 70 mph at 6 A.M. At 8 A.M. the freight train headed south from the same station at 30 mph. At what time will the trains be 440 mi apart? Example 46 At 4 A.M. the northbound train left at 40 mph. At 6 A.M. the southbound train left the same station at 60 mph. At what time will the trains be 880 mi apart? Example 47 The northbound bus had been on the road at 50 mph for 4 hours before the southbound bus left the same station at 45 mph. How long was the southbound bus on the road before the buses were 580 mi apart? Example 48 The freight train headed south at 9 A.M., and the express train headed north from the same station at noon. At 3 P.M., the trains were 420 mi apart. What was the speed of each if the speed of the express train was 20 mph greater than the speed of the freight train?
Uniform Motion Problems Of Unequal Distances Example 49 At 8 P.M. Achilles left camp and headed south at 20 kph. At 10 P.M. Patroclos headed south from the same camp. If Patroclos was 50 km ahead by 3 A.M., what was his speed? Example 50 Rachel has a 15 km head start on Charlene. How long will it take Charlene to catch Rachel if Rachel travels 70 kph and Charlene travels at 100 kph? Example 51 Harry and Jennet jog around a circular track that is 210 m long. Jennet s rate is 230 m per minute, while Harry s rate is only 200 m per minute. In how many minutes will Jennet be a full lap ahead? Example 52 At 5 A.M. Napoleon headed south from Waterloo at 4 kph. At 7 A.M. Wellington headed south from Waterloo. If Wellington passes Napoleon and was 20 km ahead of Napoleon at 2 P.M., how fast was Wellington traveling? Example 53 Helen has 4 km head start on Paris. How long will it take Paris to catch Helen if Helen travels at 6 kph and Paris travels at 8 kph? Example 54 Ferris and Julia jog around a circular track that is 500 m long. Julia s rate is 250 m per minute, while Ferris rate is only 230 m per minute. In how many minutes will Julia be a full lap ahead? Example 55 Eleanor started out at 60 mph at 9 A.M., two hours before Alexi started out to catch her. If she was still 60 mi ahead at 3 P.M., how fast was Alexi driving? Example 56 Boesch had a 40 m head start. How long did it take Louis to catch up if Louis traveled at 10 m per second while Boesch traveled at only 6 m per second>
Example 57 At the pole My Bequest was only 40 ft behind Flying Lady. How long did it take My Bequest running at 54 ft per second to catch Flying Lady running at 46 ft per second? Example 58 Roger Goose had a 500 yd head start on Willa. If Willa s speed was 40 yd per second and Roger s speed was only 20 yd per second, how long did it take Willa to catch up? Example 59 Soren had a 36 mi head start. If Erik caught him in 3 hours, how fast was Erik traveling if his speed was twice that of Soren s? Example 60 The gun sounded, and 3 hours later Bill was 6 mi ahead of Rose. How fast did Rose run if Bill s speed was 10 mph? Example 61 The brigantine was sailing at full speed and was 30 mi at sea when Lord Nelson began to give chase at twice the speed of the brigantine. if Nelson caught up in 6 hours, how fast was the brigantine traveling? Example 62 The freight train headed north at 9 A.M. at 40 mph. Two hours later, the express train headed north at 60 mph. What time was it when the express was 20 mi further from the town than the freight? Example 63 Homer drove as fast as he could to get 60 mi ahead of Mae. If Homer drove at 17 mph and accomplished his goal 20 hours after they both began, how fast did Mae drive?