Two trains are moving toward or away from Centerville. Their distances (in miles) from Centerville at time t hours after 12:00 noon are given by: TrainDistance from Centerville (miles) Freight train-10t + 115 Passenger train-20t + 150 At what clock time will both trains be at the same distance from Centerville?

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GRE Quantitative Reasoning QUESTION #8181

Question 1

Two trains are moving toward or away from Centerville. Their distances (in miles) from Centerville at time $t$ hours after 12:00 noon are given by:

Train	Distance from Centerville (miles)
Freight train	$-10t + 115$
Passenger train	$-20t + 150$

At what clock time will both trains be at the same distance from Centerville?

Correct Answer Explanation

Set the two distance expressions equal:

$-10t + 115 = -20t + 150$

$-10t + 20t = 150 - 115$

$10t = 35$

$t = 3.5$ hours after 12:00 noon $= 3$ hours and $30$ minutes after noon $= \mathbf{3{:}30}$ PM.