HKD1710 wrote:

Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes. They work together for 30 minutes then Jim goes fishing and Larry finishes the job. How long did Larry have to work?

A) 15 min.

B) 75 min.

C) 42 min.

D) 45 min.

E) 20 min.

Source: 800Score

To solve for the

extra time Larry had to work, I converted from minutes to hours, solved, then converted back to minutes for answer.

(Not the quickest for some people. There are many ways to solve this problem - proportion, LCM, others)

Convert minutes to hoursMultiply each rate by 60 (\(\frac{mins}{hr})\)

L's rate = \(\frac{1}{90} mins\) * 60 = \(\frac{2}{3}\)hr

J's rate = \(\frac{1}{60}\) * 60 = \(\frac{1}{1}\)

Add both rates for the rate at which they work together:

\(\frac{2}{3}\) + 1 = \(\frac{5}{3}\) is combined rate in \(\frac{gardens}{hour}\)

The amount of work they finish together in 30 minutes = \(\frac{1}{2}\)hr?

rt = W

\(\frac{5}{3}\) * \(\frac{1}{2}\)= \(\frac{5}{6}\) of work finished when Jim leaves

\(\frac{1}{6}\) of work remains for Larry. \(\frac{W}{r} =

t\):

\(\frac{\frac{1}{6}}{\frac{2}{3}}\)* =

\(\frac{1}{6}\) * \(\frac{3}{2}\) =

\(\frac{1}{4}\) of an hour for Larry to finish.

Convert back: \(\frac{1}{4}\) * 60 = 15 minutes

Larry worked 30 minutes with Jim. Larry worked 15 minutes alone. Larry worked 45 minutes total.

ANSWER D

Minutes onlyL's rate = \(\frac{1}{90}\)

J's rate = \(\frac{1}{60}\)

Add rates for time worked together

(\(\frac{1}{90}\) + \(\frac{1}{60}\)) =\((\frac{150}{5400})\) = \(\frac{1}{36}\) is combined rate

Work finished together:

\(\frac{1}{36}\) * 30 mins = \(\frac{30}{36}\) = \(\frac{5}{6}\) finished,

and \(\frac{1}{6}\) remains for Larry

W/r = t, so Larry needs

\(\frac{\frac{1}{6}}{\frac{1}{90}}\) =

\(\frac{1}{6}\) * \(\frac{90}{1}\) = 15 minutes to finish

Larry with Jim: 30 minutes of work. Larry alone: 15 minutes. Larry had to work 45 minutes.

ANSWER D

Edited to correct answer from A to D. (A is time to finish, D is total time.) Analysis re extra time is still accurate. Kudos to @pawai1989.
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