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James started from his home and drove eastwards at a

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James started from his home and drove eastwards at a

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Source: e-GMAT

James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated 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%

The OA is D.

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BTGmoderatorLU wrote:
Source: e-GMAT

James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated 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%
Let James' rate = 3 mph.

James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated 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.
When James is overtaken by Patrick, James has traveled for a total of 3 hours, implying the following distance:
rt = 3*3 = 9 miles.
Patrick leaves 90 minutes after James and thus overtakes James by traveling these 9 miles in only 1.5 hours, implying the following rate for Patrick:
d/t = 9/(1.5) = 90/15 = 6 mph.

Patrick then continued driving at the same speed for another 2 hours.
When people COMPETE, we SUBTRACT THEIR RATES.
Difference between Patrick's rate and James' rate = 6-3 = 3 mph.
Implication:
Every hour after overtaking James, Patrick travels 3 miles ahead of James.
Thus:
Over the next 2 hours, Patrick travels a total of 6 miles head of James.

By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?
Since 2 hours have passed since Patrick overtook James, James must catch up to Patrick in the next 6 hours.
Implication:
For James to catch up by 6 miles over the next 6 hours, he must catch up by 1 mile every hour.
Thus:
Over the next 6 hours, James' rate must be ONE MPH GREATER than Patrick's rate, so that James catches up by 1 mile every hour.
Since James' rate = 3 mph, Patrick's rate must decrease from 6 mph to 2 mph.
Percent decrease from 6 to 2 = Difference/Larger * 100 = (6-2)/6 * 100 = 66.66%.

The correct answer is D.

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BTGmoderatorLU wrote:
Source: e-GMAT

James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated 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%

The OA is D.
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 slower 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

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