mc563427 wrote:

If two trains are 120 miles apart and are traveling toward each other at constant rate of 30 miles per hour and 40 miles per hour, respectively, how far apart will they be 1 hour before they meet?

(A) 10

(B) 30

(C) 40

(D) 50

(E) 70

Since we have a converging rate problem, we can use the following formula:

distance 1 train + distance 2 train = total distance

We can let t be the time the two trains will meet. Thus:

30t + 40t = 120

70t = 120

t = 120/70 = 12/7 hours

Since we want to find the distance apart 1 hour before they meet, the distance traveled by one train is 30(12/7 - 1) = 30(5/7) = 150/7 miles and the distance traveled by the other train is 40(12/7 - 1) = 40(5/7) = 200/7 miles. Thus, the total distance traveled by the two trains is 150/7 + 200/7 = 350/7 = 50 miles. Therefore, they are 120 - 50 = 70 miles apart 1 hour before they meet.

Alternative solution:

A much shorter approach to solve this problem is to argue the following:

Since in 1 hour, train 1 travels 30 miles and train 2 travels 40 miles, 1 hour before they meet, they should be 30 + 40 = 70 miles apart.

Answer: E

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