1) A motor boat, traveling 10 miles per hour, left a marina. After three hours, a speed boat going 30 miles per hour began to follow the motor boat. How long did it take the speed boat to overtake the motor boat? D(motor boat) = D(speed boat) 10(t + 3)= 30t The answer is 1 and 1/2 hours. 2) Jerry, walking 5 miles per hour, started toward his aunt’s house 12 miles away. Thirty minutes later, his cousin Darryl started from the aunt’s house on his bike to meet him, riding 10 miles per hour. How long will Darryl ride before he meets Jerry? Jerry’s Distance + Darryl’s Distance = 12 miles 5t + 10(t – ½) = 12 The answer is 38 minutes. 3) Two friends leave a hotel at the same time traveling in opposite directions. They travel for four hours and are then 480 miles apart. If Susan travels 10 miles per hour faster than Joan, find the average rate of speed for each person. Susan’s distance + Joan’s distance = 480 4(r + 10) + 4r = 480 The answer is Joan’s speed is 55 mph and Susan’s speed is 65 mph. 4) A runner decides to run out to Bristol. He begins to run at an average rate of 9 miles per hour. He runs a certain distance and then turns around and returns along the same route at an average rate of 6 miles per hour. If the round trip took 2 and a half hours, how far did the runner travel before turning around? Distance to Bristol = Distance from Bristol 9t = 6(2.5 – t) 9t = 15 – 6t T = 1 hour, so… The answer is 9 miles. 5) Two students on bicycles leave their classroom building at 10:00 AM and travel in opposite directions. If the average speed of one of the students is 12 kilometers per hour and the average speed of the other student is 14 kilometers per hour, at what time will they be 65 kilometers apart? Distance 1 + Distance 2 = 65 km 12t + 14t = 65 T = 2.5 hours, so… The answer is 12:30 P.M. 6) James leaves his home town traveling 70 miles per hour. At the same time Paul leaves home traveling 75 miles per hour. The two live 580 miles apart and are traveling to meet each other for a lunch meeting at noon. What time did they leave their homes? James’ Distance + Paul’s Distance = 580 70t + 75t = 580 T = 4 hours, so… The answer is 8 A.M. 7) Kansas city and Denver are 330 miles apart. Two cars start from these cities traveling toward each other. They meet after 3 hours. Find the rate of each car if one travels 20 mph slower than the other. Distance towards KC + Distance towards Denver = 330 3r + 3(r – 20) = 330 The answer is 45 mph and 65 mph. 8) Two trains are 150 miles apart and are traveling toward each other. If one train is going twice as fast as the other and they will meet in two hours, how fast is the faster train going? 2r + 4r = 150 The answer is 50 mph. 9) Two cars leave town at the same time traveling in opposite directions. One car travels at a rate of 60 miles per hour. The other car travels at a rate of 70 miles per hour. How far apart will the two cars be at the end of 4 hours? Hint: Yes, this is REALLY easy! Just find the distance each one travels. 60mph times 4 hours = 240 miles 70mph times 4 hours = 280 miles 280 miles + 240 miles = 520 miles The answer is 520 miles. 10) John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 58. How old is John now? Hint: Let Alice’s age = a, John’s age = 2a, dad’s age = 10a. In two years, they will all be two years older, so add two to each “current age”. In 2 years, Alice’s age = a + 2, John’s age = 2a + 2, dad’s age = 10a + 2. The sum of their “future” ages is 58, so add them all together. (a + 2) + (2a + 2) + (10a + 2) = 58 13a + 6 = 58 13a = 52 a = 4…so Alice is 4 years old. The answer, John is currently 8.