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# Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes

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Director
Joined: 22 Jun 2014
Posts: 897

Kudos [?]: 420 [1], given: 111

Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes [#permalink]

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02 Sep 2017, 10:21
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4
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Difficulty:

85% (hard)

Question Stats:

40% (01:34) correct 60% (01:15) wrong based on 77 sessions

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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
[Reveal] Spoiler: OA

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Kudos [?]: 420 [1], given: 111

Manager
Joined: 21 Feb 2017
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Re: Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes [#permalink]

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02 Sep 2017, 10:32
Option A.

By working together they can finish 1 job in 180/5 minutes. So in 30 minutes they can complete 5/6 work. Now remaining 1/6 work will be completed by Larry in 90/6=15 minutes.

Sent from my XT1663 using GMAT Club Forum mobile app

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Director
Joined: 22 May 2016
Posts: 802

Kudos [?]: 253 [0], given: 544

Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes [#permalink]

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03 Sep 2017, 10:50
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 hours

Multiply 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.

Minutes only

L'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.

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.

Last edited by genxer123 on 04 Sep 2017, 08:56, edited 1 time in total.

Kudos [?]: 253 [0], given: 544

Manager
Joined: 07 Jun 2017
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Re: Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes [#permalink]

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03 Sep 2017, 19:05
Why the answer is not A?
Dear Bunuel or anyone, would you explain?

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Intern
Joined: 22 Aug 2017
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Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes [#permalink]

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03 Sep 2017, 19:42
1
KUDOS
Let the total lawn area be X.
Larry needs 90 mins to hoe X. So in 30 mins Larry can hoe X/3.
Jim needs 60 mins to hoe X, So in 30 mins Jim can hoe X/2.
Therefore, both of them together can hoe X/3+X/2 = 5X/6 in 30 mins.
Remaining part to hoe is X-5X/6=X/6

We know Larry needs 90 mins to hoe X. So she will need X/6*90 = 15 mins to hoe remaining part.
So Larry's total time = 30mins +additional 15 mins = 45 mins

Kudos [?]: 1 [1], given: 2

Manager
Joined: 07 Jun 2017
Posts: 111

Kudos [?]: 3 [0], given: 454

Re: Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes [#permalink]

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03 Sep 2017, 19:49
pawai1989 wrote:
Let the total lawn area be X.
Larry needs 90 mins to hoe X. So in 30 mins Larry can hoe X/3.
Jim needs 60 mins to hoe X, So in 30 mins Jim can hoe X/2.
Therefore, both of them together can hoe X/3+X/2 = 5X/6 in 30 mins.
Remaining part to hoe is X-5X/6=X/6

We know Larry needs 90 mins to hoe X. So she will need X/6*90 = 15 mins to hoe remaining part.
So Larry's total time = 30mins +additional 15 mins = 45 mins

The question is asking Larry's total time, not remaining time?
I think that made most people confused

Kudos [?]: 3 [0], given: 454

Senior Manager
Joined: 02 Jul 2017
Posts: 252

Kudos [?]: 59 [0], given: 59

Location: India
Re: Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes [#permalink]

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04 Sep 2017, 00:36
Lary takes 90 min to finish 1 job
Jim takes 60 min to finish 1 job.

They worked for 30 mins together.
So lary => 90 min =1 job => 30 min = (1/90)*30 = 1/3rd of job
So Jim => 60 min =1 job => 30 min = (1/60)*30 = 1/2 of job

So total job finished in 30 mins = 1/3 + 1/2 = 5/6 work
Remaing work = 1/6

This work is done by Lary alone
lary => 1 job = 90 mins => 1/6 job = 90 * (1/6) = 15 mins

So job got finished in 15 mins after Jim left.

Total time Lary worked = 30+ 15 = 45 mins

Kudos [?]: 59 [0], given: 59

Director
Joined: 22 May 2016
Posts: 802

Kudos [?]: 253 [1], given: 544

Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes [#permalink]

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04 Sep 2017, 08:30
1
KUDOS
Quote:
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.

pclawong wrote:
pawai1989 wrote:
Let the total lawn area be X.
Larry needs 90 mins to hoe X. So in 30 mins Larry can hoe X/3.
Jim needs 60 mins to hoe X, So in 30 mins Jim can hoe X/2.
Therefore, both of them together can hoe X/3+X/2 = 5X/6 in 30 mins.
Remaining part to hoe is X-5X/6=X/6

We know Larry needs 90 mins to hoe X. So she will need X/6*90 = 15 mins to hoe remaining part.
So Larry's total time = 30mins +additional 15 mins = 45 mins

The question is asking Larry's total time, not remaining time?
I think that made most people confused

pclawong: Yes, the question asks for Larry's TOTAL work time, which I and others missed.

I think the question is fair: "How long did Larry have to work?"

It does not ask how long Larry had to work to finish, just how long he had to "work." It's a "trap" I've seen before.

Kudos given to pawai1989

Kudos [?]: 253 [1], given: 544

Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes   [#permalink] 04 Sep 2017, 08:30
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