GMAT Question of the Week #5: Problem Solving

Writing on chalk board in black and white

Solve the problem and indicate the best of the answer choices given.

If a freight train travels at an average speed of 30 mph, it will arrive at its destination 1.5 hours late. If the train instead travels at an average speed of 45 mph, it will arrive 1 hour early. At what average speed, in miles per hour, should the train travel in order to arrive at its destination exactly on time?

A) 33
B) 35
C) 36
D) 37.5
E) 39

Click here for the answer and explanation.
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Explanation

We have two speeds and two times, and both trips cover the same distance. Using the given speeds 30 and 45, times t+1.5 and t-1, respectively, (where t is the time required for an on-time arrival), and that both distances are equal, we can write and solve an equation to determine t :

30(t+1.5)=45(t-1)

30t+45=45t-45

90=15t

t=6

To find the average speed the train should travel to arrive on time, first let’s determine the distance the train travels. We can useĀ t=6 and one of the given rates and times. Let’s choose 30(t+1.5).

30(6+1.5)=30(7.5)=225 miles

So, if the train travels 225 miles and arrives on time in 6 hours, then the average speed the train should travel is \tfrac{225}{6}=37.5 miles per hour.

The correct answer is Choice (D).

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