Problem Solving

LUANDATO 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

Alternate Solution:

At the time when Carla begins driving, Richard has been driving for 30 minutes = 0.5 hours; thus he has covered a distance of 30 x 0.5 = 15 miles. So, when Carla begins driving, the distance between them is 15 miles. If Carla is to catch Richard 3 hours after she begins driving, the distance between the two must decrease by 15 / 3 = 5 miles every hour. This means that Carla should drive 5 mph faster than Richard, i.e. 30 + 5 = 35 mph.

Answer: A