Manonamission
Train X is travelling at a constant speed of 30 miles per hour and Train Y is travelling at a constant speed of 40 miles per hour. If the two trains are travelling in the same direction along the same route but Train X is 25 miles ahead of Train Y, how many hours will it be until Train Y is 10 miles ahead of Train X?
A. 1.5
B. 2.0
C. 2.5
D. 3.0
E. 3.5
This is a "chase" question. One approach is the "gap" method.
The distance between Trains X and Y is the gap.
In "chase" problems (one traveler is behind another and needs to catch up), the
relative rate, R used is (Faster - Slower)
Distance here? Y is 25 miles behind X,
andY needs to get 10 miles ahead of X
25 + 10 = 35 miles (= gap)
Relative rate (speed)?Y is faster than X. Y catches and passes X.
Use relative speed (Faster - Slower) = (Y - X)
Rate = (40 mph - 30mph) = 10 mph = \(R\)
That's the rate (speed) at which the gap closes.*
Time required to cover that distance/close the gap?
\(R * T = D\), and \(T=\frac{D}{R}\)\(Time = \frac{D}{R}=\frac{35mi}{10mph}=3.5\) hours
Answer E
*Y actually closes the gap. X and Y both move. Y moves faster. The rate at which Y closes the gap is Y's speed - X's speed.