Randle can trim 4 bushes an hour and Billy can trim 5 bushes an hour.

Question

Randle can trim 4 bushes an hour and Billy can trim 5 bushes an hour. If the two together must trim all 50 bushes in the park and each person can trim for a maximum of 6 hours, what is the least amount of time that Billy must trim?

A. 4 hours 33 minutes
B. 4 hours 48 minutes
C. 5 hours
D. 5 hours 12 minutes
E. 6 hours

A. 4 hours 33 minutes
B. 4 hours 48 minutes
C. 5 hours
D. 5 hours 12 minutes
E. 6 hours

BrentGMATPrepNow · Answer

To MINIMIZE Billy's work time, we must MAXIMIZE Randle's work time.

So, let's first let Randle work the full 6 hours and see how many bushes are left for Billy to trim. 
Output = (rate)(time)
Randle's rate is 4 bushes an hour.
So, in 6 hours, Randle's output = (4 bushes per hour)(6 hours) = 24
So, Randle will trim a total of 24 bushes.

There are 50 bushes in the park. So, if Randle trims 24 of them, then Billy must trim the remaining  26  bushes. 
Time = output/rate
Billy's rate is 5 bushes an hour
So Billy's work time =  26 /(5 bushes per hour) = 5.2 hours

NOTE: since answer choice D is the only option that's between 5 and 6 hours, it must be the correct answer.

Answer: D

eddy8700 · Answer

Answer is D

Together they can work at rate of 9 bushes /hr
to minimize the no of hours billy should work randle has to be maximized i.e 4*6=24 bushes
remaining 26 bushes need to be produced by Billy
26/5 so it would greater than 5 but less than 6

JeffTargetTestPrep · Answer

Since Randle can trim 4 bushes an hour and Billy can trim 5 bushes an hour, Randle’s rate is 4 and Billy’s rate is 5. We are also given that they must trim 50 bushes together and each person can trim for a maximum of 6 hours. We need to determine the least amount of time that Billy must trim. Thus, we want to maximize the time Randle trims the bushes. So, let’s say Randle uses all 6 hours of trimming (since that is the maximum time each person can use), and thus create the following equation in which t is the (least amount of) time Billy uses to trim the bushes:

4(6) + 5t = 50

24 + 5t = 50

5t = 26

t = 26/5 = 5⅕ hours

Since ⅕ of an hour is 12 minutes, the least amount of time Billy can trim is 5 hours and 12 minutes.

Answer: D

EgmatQuantExpert · Answer

Solution

• Randle can trim  4  bushes in an hour.

• Billy can trim  5  bushes in an hour.

• We need to trim  50  bushes.

o But each person can work for  6  hours only.

• And  Billy needs to work for the least amount of time .

o Thus, Randle will work for full  6  hours, in which he can trim  = 4*6 = 24  bushes.

• But we need  50  bushes, these remaining 26 bushes can be trimmed by Billy in  = \frac{(26)}{5} hour = 5 hours  \frac{1}{5}*60  mins = 5  hours  12  mins.

• Hence, correct answer is   Option D  .

Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant ? Attend this webinar on   2nd April   to learn a structured approach to  solve 700+ Number Properties question in less than 2 minutes .  Register

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Randle can trim 4 bushes an hour and Billy can trim 5 bushes an hour.

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Randle can trim 4 bushes an hour and Billy can trim 5 bushes an hour.

Prep Toolkit

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