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# Barry builds sand castles 50% faster than Michelle. If it takes Michel

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Re: Barry builds sand castles 50% faster than Michelle. If it takes Michel [#permalink]
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Bunuel wrote:
Barry builds sand castles 50% faster than Michelle. If it takes Michelle 48 minutes to build a sand castle, how many minutes does it take Barry to build a sand castle?

A. 16
B. 20
C. 24
D. 32
E. 40

Solution:

Let Michelle’s rate = r, then Barry’s rate = 1.5r. Since Michelle’s time is 48 minutes and time = job/rate, we have 48 = 1/r and hence r = 1/48 and 1.5r = 3/2 x 1/48 = 1/32. Therefore, Barry’s time is 1/(1/32) = 32 minutes.

Alternate Solution:

In 96 minutes, Michelle can build 96/48 = 2 sand castles. Since Barry builds sand castles 50% faster than Michelle, he will build 2 * (1 + 50/100) = 2 * 150/100 = 3 sand castles. Since Barry can build 3 sand castles in 96 minutes, he can build one sand castle in 96/3 = 32 minutes.

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Re: Barry builds sand castles 50% faster than Michelle. If it takes Michel [#permalink]
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Q: Barry builds sand castles 50% faster than Michelle. If it takes Michelle 48 minutes to build a sand castle, how many minutes does it take Barry to build a sand castle?

Ans: Rate of Barry = 50%* Rate of Michelle + Rate of Michelle
= 1.5 * Rate of Michelle
= 1.5 * (1/48)
= 1/32

Time taken by Barry = 32 mins
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Re: Barry builds sand castles 50% faster than Michelle. If it takes Michel [#permalink]
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Re: Barry builds sand castles 50% faster than Michelle. If it takes Michel [#permalink]
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