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 GMAT Test Question (question 4 of 6)

GMAT Test Question (Hard Difficulty) from 800score

Jeff and Tim are 120 miles apart. They begin bicycling toward each other. Jeff travels at 30 mph. Tim travels at a rate of 20 mph. If they begin at 6 a.m., at what time do they meet?

a) 7:30 a.m.
b) 7:48 a.m.
c) 8:24 a.m.
d) 8:36 a.m.
e) 9:12 a.m.

The distance between two oppositely traveling objects is diminishing at a rate equal to the sum of the rates of the two moving objects, because they are closing in on each other. Since Jeff is traveling at 30 mph and Tim is traveling at 20 mph, the distance between them is closing at a rate of 30 + 20 = 50 mph .

Now we want to substitute our given distance, 120 miles, and our rate, 50 mph, into the rate formula to find time it takes for Jeff and Tim to meet.

Distance = Rate × Time

Rearranging this formula to solve for Time, we get:

 Time = Distance Rate

 Time = 120 miles 50 mph

Time = 2.4 hours

0.4 hours is 60 × 0.4 = 24 minutes. So Time = 2 hours and 24 minutes.

Since the bicyclists begin at 6 a.m. and it takes them 2 hours and 24 minutes to meet, then they meet at 8:24 a.m. The correct answer is C.

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