GRE,CAT,GMAT,QUANTITATIVE - SPEED , TIME AND DISTANCE

Question A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters? 240 meters 360 meters 420 meters 600 meters Cannot be determined The correct choice is (A) and the correct answer is 240 meters. Explanatory Answer When the train crosses a man standing on a platform, the distance covered by the train is equal to the length of the train.However, when the same train crosses a platform, the distance covered by the train is equal to the length of the train plus the length of the platform.The extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover = length of the platform.Therefore, length of the platform = speed of train * extra time taken to cross the platformLength of platform = 72 kmph * 12 secondsConverting 72 kmph into m/sec, we get 72 kmph = = 20 m/secTherefore, length of the platform = 20 * 12 = 240 meters. Question Jim travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Jim's travel in mph? 42 mph 36 mph 37.5 mph 42.5 mph 48 mph The correct choice is (C) and the correct answer is 37.5 mph. Explanatory Answer Average speed = Total distance traveled by Jim = Distance covered in the first 3 hours + Distance covered in the next 5 hours.Distance covered in the first 3 hours = 3 * 60 = 180 milesDistance covered in the next 5 hours = 5 * 24 = 120 milesTherefore, total distance traveled = 180 + 120 = 300 miles.Total time taken = 3 + 5 = 8 hours.Average speed = = 37.5 mph. Question Jane covered a distance of 340 miles between city A and city taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour? 2 hours 30 minutes 3 hours 2 hours 1 hour 45 minutes None of these The correct choice is (B) and the correct answer is 3 hours. Explanatory Answer Let 'x' hours be the time for which Jane traveled at 60 miles per hour.As the total time taken to cover 340 miles is 5 hours, Jane would have traveled (5 - x) hours at 80 miles per hour.Distance covered at 60 miles per hour = Speed * time = 60 * x = 60x milesDistance covered at 80 miles per hour = Speed * time = 80 (5 - x) = 400 - 80x milesTotal distance covered = Distance covered at 60 miles per hour + Distance covered at 80 miles per hour.Therefore, total distance = 60x + 400 - 80x.But, we know that the total distance = 340 miles.Therefore, 340 = 60x + 400 - 80x => 20x = 60 or x = 3 hours. Question A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat. What is the length of the race? 10 meters 25 meters 45 meters 15 meters 35 meters The correct choice is (E) and the correct answer is 35 meters. Explanatory Answer A runs 25% as fast as B.That is, if B runs 100m in a given time, then A will run 125m in the same timeIn other words, if A runs 5m in a given time, then B will run 4m in the same time.Therefore, if the length of a race is 5m, then A can give B a start of 1m so that they finish the race in a dead heat.Start : length of race :: 1 : 5In this question, we know that the start is 7m.Hence, the length of the race will be 7 * 5 = 35m.