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john would have reduced the time

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by abhasjha » Wed Jun 04, 2014 9:58 am
John would have reduced the time it took him to drive from his home to a certain store by 1/3 if he had increased his average speed by 15 miles per hour. What was John's actual average speed, in miles per hour, when he drove from his home to the store?

(A) 25
(B) 30
(C) 40
(D) 45
(E) 50

looking for some quicker method .....
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by sukriti2hats » Wed Jun 04, 2014 10:31 am
abhasjha wrote:John would have reduced the time it took him to drive from his home to a certain store by 1/3 if he had increased his average speed by 15 miles per hour. What was John's actual average speed, in miles per hour, when he drove from his home to the store?

(A) 25
(B) 30
(C) 40
(D) 45
(E) 50

looking for some quicker method .....
Hi abhasjha,

In this problem, distance remains constant.
Initially d = s x t
After time is reduced by 1/3rd and speed increased by 15: d= (t-t/3) x (s+15)
Equate both (since distance is constant in both cases) : s x t = (2t/3) x (s+15)
S =30

Regards
Sukriti
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by GMATGuruNY » Wed Jun 04, 2014 11:10 am
abhasjha wrote:John would have reduced the time it took him to drive from his home to a certain store by 1/3 if he had increased his average speed by 15 miles per hour. What was John's actual average speed, in miles per hour, when he drove from his home to the store?

(A) 25
(B) 30
(C) 40
(D) 45
(E) 50
Since the time is reduced by 1/3, the faster time is 2/3 of the actual time.
Time and rate are RECIPROCALS.
2/3 of the actual time implies 3/2 of the actual speed.
In other words, John increased his speed by 50%.
Thus, the increase in the speed -- 15mph -- must be equal to 50% of the actual speed, implying that the actual speed = 30mph.

The correct answer is B.
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by [email protected] » Wed Jun 04, 2014 5:14 pm
Hi abhasjha,

This question is perfect for TESTing THE ANSWERS.

Since you're not given a "distance" to work with, you can choose whatever distance you'd like, then plug in the answers until you find the one that matches the information in the prompt.

From a Number Property standpoint, the correct answer is likely to be a multiple of 15, since increasing the speed by 15 reduced the drive time by exactly 1/3 (and not some weird decimal).

Since B and D are both multiples of 15, we can choose either to start with. I'll go with B first because the math will be easier.

We'll test what happens with the speed equals 30mph and when it equals 30+15=45mph. I'll set the distance = 90 miles, since 90 is a multiple of both 30 and 45.

D = R x T
90 = 30(3 hours)
90 = 45(2 hours)

Here, time is reduced by 1/3, which is a MATCH for the information in the prompt. This MUST be the correct answer.

Final Answer: B

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