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A certain vehicle is undergoing performance adjustments during a set

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A certain vehicle is undergoing performance adjustments during a set [#permalink]

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New post 28 Aug 2015, 02:14
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A certain vehicle is undergoing performance adjustments during a set of three trials on an 8-mile track. The first time it travels around the track at a constant rate of p miles per minute, the second time at a constant rate of p^2 miles per minute, and the third time at a constant rate of p^3 miles per minute. If the vehicle takes the same time to travel the first 18 miles of these trials as it does to travel the last 8 miles, how many minutes does it take to complete all three trials (not counting any time between trials)?


(A) 18
(B) 36
(C) 60
(D) 96
(E) 112

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[Reveal] Spoiler: OA

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New post 28 Aug 2015, 09:55
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Bunuel wrote:
A certain vehicle is undergoing performance adjustments during a set of three trials on an 8-mile track. The first time it travels around the track at a constant rate of p miles per minute, the second time at a constant rate of p^2 miles per minute, and the third time at a constant rate of p^3 miles per minute. If the vehicle takes the same time to travel the first 18 miles of these trials as it does to travel the last 8 miles, how many minutes does it take to complete all three trials (not counting any time between trials)?


(A) 18
(B) 36
(C) 60
(D) 96
(E) 112

Kudos for a correct solution.

1. Time taken for first 18 miles = \(\frac{8}{p} + \frac{8}{p^2}+\frac{2}{p^3}\)
2. For the last 8 miles =\(\frac{8}{p^3}\)
As per the problem,
\(\frac{8}{p} + \frac{8}{p^2}+\frac{2}{p^3}\)= \(\frac{8}{p^3}\)
Solving for p,
p=\(\frac{1}{2}\)

Therefore, time taken for all the 3 trials =\(\frac{8}{(1/2)} +\frac{8}{(1/4)} +\frac{8}{(1/8)}\) = 16 +32 + 64 = 112
Ans: E

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A certain vehicle is undergoing performance adjustments during a set [#permalink]

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New post 29 Aug 2015, 21:47
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This is a rate-time-distance problem. We would be better off setting a rate-time-distance table.

The first journey takes 18 miles whereas the last journey takes 8 miles.

We are told that:
r1= p
r2=p^2
and r3= p^3 so we set up a table like

r x t = d
p x t1 = 8
p^2 x t2= 8
p^3 x t3 = 2 (because 18-16)

so the time taken to complete each leg individually amounts to t1 + t2 + t3 = (8/p) + (8/p^2) + (2/p^3). ----> (equation 1)

On the other hand, the time taken to complete the last leg of miles is (8/p^3) ---> (equation 2) because p^3 is the speed on the last leg. Since both the times are equal, equate them to get:

(8/p) + (8/p^2) + (2/p^3) = (8/p^3)

Taking the LCM of the Left hand equation and solving both these equations gives us the value of p=1/2 and p= (-3/2) Since p can not be negative, we have p=1/2 as our value.

Now put this value in the time taken to finish each trial which is the sume of (8/p) + (8/p^2) + (8/p^3) and it will become 16+32+64 = 112 minutes.
Option E is the correct answer.

p.s: if you like the explanation, please give a kudos :)

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New post 20 Sep 2017, 04:40
Hi, I had a doubt on this question. As per my understanding, it is said "If the vehicle takes the same time to travel the first 18 miles of these trials" and then "the last 8 miles" Adding the above two cases(18+8=26) but the total length is (8*3=24)miles. How is this possible. Please let me know

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Re: A certain vehicle is undergoing performance adjustments during a set [#permalink]

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New post 20 Sep 2017, 04:50
Tapabrata18 wrote:
Hi, I had a doubt on this question. As per my understanding, it is said "If the vehicle takes the same time to travel the first 18 miles of these trials" and then "the last 8 miles" Adding the above two cases(18+8=26) but the total length is (8*3=24)miles. How is this possible. Please let me know


The first 18 miles consists of 8 miles of the first trial + 8 miles of the second trial + the first 2 miles of the third trial. The last 8 miles consists of 8 miles of the third trial. So, there is an overlap of 2 miles.
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New to the Math Forum?
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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Kudos [?]: 128902 [0], given: 12183

Re: A certain vehicle is undergoing performance adjustments during a set   [#permalink] 20 Sep 2017, 04:50
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