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

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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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02 Sep 2017, 10:21
3
5
00:00

Difficulty:

65% (hard)

Question Stats:

52% (01:44) correct 48% (01:55) wrong based on 119 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

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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
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

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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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04 Sep 2017, 08:30
1
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
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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.

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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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Updated on: 04 Sep 2017, 08:56
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.
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Originally posted by generis on 03 Sep 2017, 10:50.
Last edited by generis on 04 Sep 2017, 08:56, edited 1 time in total.
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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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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
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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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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

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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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16 Sep 2019, 08:20
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

The usual approach:
Assume total work to be 5400 units.
L=60 units per minute and J=90 units per minute
In one minute, together they do 150 units. In 30 minutes they will do 4500.
Remaining work=900
L will take 900/60=15 minutes.

Total time taken by L=30+15=45 mins.

As generis already pointed out, this is a common known trap.

Thank you!
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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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20 Sep 2019, 17:41
pclawong wrote:
Why the answer is not A?
Dear Bunuel or anyone, would you explain?

Because, THE TOTAL TIME TAKEN BY LARRY TO DO THE JOB IS ASKED THERE...NOT, THE REMAINING TIME. SO, CAREFUL!!!

Posted from my mobile device
Re: Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes   [#permalink] 20 Sep 2019, 17:41
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