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A certain vehicle is undergoing performance adjustments during a set
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28 Aug 2015, 02:14
28 Aug 2015, 02:14
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Expert Reply
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A
B
C
D
E
Difficulty:
75%
(hard)
Question Stats:
64% (03:31) correct
36%
(03:07)
wrong
based on 118
sessions
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.
(A) 18
(B) 36
(C) 60
(D) 96
(E) 112
Kudos for a correct solution.
Re: A certain vehicle is undergoing performance adjustments during a set
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28 Aug 2015, 09:55
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.
(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
General Discussion
A certain vehicle is undergoing performance adjustments during a set
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29 Aug 2015, 21:47
29 Aug 2015, 21:47
1
Kudos
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
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
