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

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

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
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