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Pat, Kate, and Mark charged a total of 162 hours to a certain project. [#permalink]

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04 Jul 2006, 04:57

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Pat, Kate, and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?

Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project. [#permalink]

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04 Jul 2006, 05:04

My solution was:

P=2K
P=(1/3)M

This gives a ratio 1:2:1/3, which is 3:6:1 (P:K:M).
TOTAL = 162 hours

According to the ratio it should be:
P=48,6 hours K=97,2 hours M=16,2 hours ----------------
TOTAL=48,6+97,2+16,2=162 hours ----------------
The answer:
97,2-16,2=81 hours (which is not one of the choices)

You may try my approach. It may be easier and may be faster.

P+M+K=162 we need to find M-K

Lets Kate charged 60 hours then Pat charged 60*2=120 hours Mark charged 3 times more than Pat or 120*3=360

Total 60+120+360=540. M-K= 360-60=300 Now look at the trick: We must have received 162 instead of 540 hours. and the difference (M-K) is 300 not one in the available answer choices.

Now guess what you need to do to obtain the correct answer choice? Exactly 162/540=3.33 , and 300/3.33=90.

P = 18 * 2 = 36 K = 18 M = 108 M - K = 108 - 18 = 90

naveenhv wrote:

Pat, Kate and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 rd as much as Mark, how many more hours did mark charge to the project than Kate?

Pat, Kate, and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?

A. 18 B. 36 C. 72 D. 90 E. 108

We can see that Kate charged the fewest hours, so... Let x =the number of hours Kate charged

Pat charged twice as much time to the project as Kate So, 2x = the number of hours Pat charged

Pat charged 1/3 as much times as Mark In other words, Mark charged THREE TIMES as much time as Pat So, 3(2x ) = the number of hours Mark charged In other words, 6x = the number of hours Mark charged

Pat, Kate and Mark charged a total of 162 hours to a certain project. We can write: x + 2x + 6x = 162 Simplify: 9x = 162 Solve: x = 18 So, Kate charged 18 hours When we plug x = 18 into 6x, we see that Mark charged 108 hours

How many more hours did Mark charge to the project than Kate? Answer = 108 - 18 = 90 = D

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Re: Pat, Kate, and Mark charged a total of 162 hours to a
[#permalink]
20 Jan 2018, 07:22