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
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.