Bunuel wrote:

Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?

A. 35

B. 55

C. 39

D. 40

E. 60

We can classify this problem as a “catch-up” rate problem, for which we use the formula:

distance of Richard = distance of Carla

We are given that Richard began driving from home on a trip averaging 30 miles per hour and that Carla leaves 30 minutes after Richard. We need to determine at what rate Carla will have to drive to catch Richard in 3 hours. We can let Carla’s rate = r.

Since Richard started 30 minutes before Carla, Richard’s time = 1/2 + 3 = 3.5 hours and Carla's time = 3 hours.

Since distance = rate x time, we can calculate each person’s distance.

Richard’s distance = 30 x 3.5 = 105 miles

Carla’s distance = r x 3 = 3r miles

We can equate the two distances and determine r.

105 = 3r

r = 35 mph

Answer: A

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Jeffery Miller

Head of GMAT Instruction

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