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the destination of Donald?

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by wallaballa2 » Sat Feb 23, 2019 12:04 pm

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B

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Difficulty—

Donald is driving at a given speed, which if quartered; it would take him 3 hours longer to reach the destination than what is the normal time. How long in miles is the destination of Donald?
(A) It would take Donald 1 hour to reach his destination if he drives at the given speed.
(B) The difference in the given and the quartered speeds of Donald is 60 miles per hour.

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Source: — Data Sufficiency |
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by jpcameron17 » Fri Mar 01, 2019 3:52 pm
Let t1 represent the time Donald takes traveling at his normal speed, and t2 represent the time he takes when his speed is quartered. Since Donald is 4 times slower when his speed is quartered, his time is 4 times as long, thus t2 = 4t1.......... (1)
We've also been told that it takes Donald 3 more hours than normal when his speed is quartered, thus t2 = t1 + 3.......... (2)
We can combine these two equations to solve for t1:
t1 + 3 = 4t1
t1 = 1
t2 = 4

Thus it takes Donald 1 hour to travel at his normal speed.

(A) It would take Donald 1 hour to reach his destination if he drives at the given speed.
This statement is restating information that we also know, thus it is not sufficient.


(B) The difference in the given and the quartered speeds of Donald is 60 miles per hour.
Let s1 represent Donald's normal speed, and s2 represent his speed when his speed is quartered. The relationship between s1 and s2 is:
s1 = s2 *4 = 4s2..... (3)
s1 = s2 + 60..... (4)
Thus:
4s2 = s2 + 60
s2 = 20
and s1 = 80

Let d represent the distance traveled, thus:
d = s1 * t1 = 80 * 1 = 80

Thus statement (B) is sufficient. The answer is (B).
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