Bunuel wrote:
Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?
(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5
Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600
The Official Guide For GMAT® Quantitative Review, 2ND EditionTime taken to meet = Total distance travelled/Relative speed
Speed of train X = 100/5 = 20 miles/hr
Speed of train Y = 100/3 = 33.3 miles/hr
Relative Speed = 20 + 33= 53 miles/hr
Distance between them = 100 miles
Time taken to meet = 100/(53) hr = 1.88 HR
bACK TO TARGET QUESTION'
How many miles had Train X traveled when it met Train Y?
dISTANCE TRAVELLED BY TRAIN X= 20 TIME =1.88
ANS= 20*1.88 =37.7 ANS A
The concept used in these questions is Relative Speed.
If two people walk in opposite directions (either towards each other or away from each other), their speed relative to each other is the sum of their speeds. e.g. If you are walking away from me at a speed of 2 miles/hr and I am walking away from you at a speed of 1 mile/hr, together we are creating a distance of 3 miles in 1 hr between us so our relative speed is 2 + 1 = 3 miles/hr
On the other hand, when two people walk in the same direction, their relative speed is the difference between their speeds.
e.g. if you are walking away from me at 1 mile/hr and I am walking towards you at 2 miles/hr, my speed relative to you is 2-1 = 1 mile/hr.