M7MBA wrote: ↑

Thu Dec 17, 2020 11:29 am

James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James started from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?

A. 25%
B. 33%
C. 50%
D. 67%
E. 75%

Answer: D

Solution:

We can let James’ speed be 60 mph. Thus, when James drove 180 minutes (or 3 hours), Patrick drove only 90 minutes. So James drove 60 x 3 = 180 miles. Although Patrick only drove 90 minutes (or 1.5 hours), he drove the same distance as James (since he overtook James exactly in 90 minutes), so Patrick drove at a speed of 180/1.5 = 120 mph. He continued at this speed for another 2 hours, which means he drove another 2 x 120 = 240 miles. He will drive another 6 hours, however, at a different speed, so that James could catch up with him exactly 8 hours after overtaking James. We can let this new speed be x. So the total distance Patrick travels is 180 + 240 + 6x = 420 + 6x.

Now let’s look at the distance James traveled. Recall that he had to catch up with Patrick exactly 8 hours after Patrick overtook him. When Patrick overtook him, each had driven 180 miles. Since James’ speed was 60 mph (and he continued to drive at that speed), then, in another 8 hours, he will have driven 60 x 8 = 480 miles. Thus the total distance James will have traveled is 180 + 480 = 660.

Now we can equate the distances traveled by the two brothers as follows:

420 + 6x = 660

6x = 240

x = 40

Since Patrick’s original speed was 120 mph and his new speed is 40 mph, he must have reduced his original speed by 2/3, or 67%.

Answer: D