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kevincan
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Lena can complete a certain task in 3 hours Updated on: 24 Mar 2026, 04:14
Originally posted by kevincan on 16 Mar 2026, 14:27.
Last edited by Bunuel on 24 Mar 2026, 04:14, edited 3 times in total.
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C
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45% (medium)

Question Stats:

78% (02:39) correct 22% (03:05) wrong based on 114 sessions

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Lena can complete a task in 3 hours and works twice as fast as Johanna. Johanna begins working on the task without Lena, and then two of them complete the task together 1 3/4 hours after Lena began working. How long did Johanna work by herself ?

A. 36 minutes
B. 40 minutes
C. 45 minutes
D. 48 minutes
E. 54 minutes
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C
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minusaliquam
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Lena can complete a certain task in 3 hours 24 Mar 2026, 03:40
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Please can someone explain how to solve this problem in 2 minutes?
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kevincan
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Lena can complete a certain task in 3 hours 24 Mar 2026, 04:07
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The question was missing up a piece of information. It has been corrected. Thanks for inquiring.
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Lena can complete a certain task in 3 hours 24 Mar 2026, 04:30
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kevincan
Lena can complete a task in 3 hours and works twice as fast as Johanna. Johanna begins working on the task without Lena, and then two of them complete the task together 1 3/4 hours after Lena began working. How long did Johanna work by herself ?

A. 36 minutes
B. 40 minutes
C. 45 minutes
D. 48 minutes
E. 54 minutes
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Lena can complete a task in 3 hrs.

The efficiency of Lena and Johanna is 2:1.

The the time ratio of Lena and Johanna = 1:2

If the ratio of 1 equals 3 hrs, then 2 equals 6 hours.

They both work for 1 (3/4) hours = (7/4) hours.

Let’s take the total work to be 6 units.

Work = Efficiency * time

The units of work completed by both Lena and Johanna in (7/4) hours is ?

(2+1)* (7/4) = 21/4 units of work is completed.

Johanna * t + (21/4) = 6

Johanna * t = 6-(21/4)

We know the efficiency of Johanna is 1.

Therefore, t = (3/4)

Converting into minutes = (3/4)*60 = 45 minutes.

Option C
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Lena can complete a certain task in 3 hours 11 Apr 2026, 18:27
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I first found 1/3+1/6=1/2 as the combined rate of L and J, then let work equal to 1. T/6+(1/2)*(7/4)=1 and solve for T and convert to minutes
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Lena can complete a certain task in 3 hours 16 Apr 2026, 02:07
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Could you pls explain the last part where you got 3/4*60 ? I got it till that part, Joanna finishes 3/4 units of the total work, but what you did there after that?
Dereno

Lena can complete a task in 3 hrs.

The efficiency of Lena and Johanna is 2:1.

The the time ratio of Lena and Johanna = 1:2

If the ratio of 1 equals 3 hrs, then 2 equals 6 hours.

They both work for 1 (3/4) hours = (7/4) hours.

Let’s take the total work to be 6 units.

Work = Efficiency * time

The units of work completed by both Lena and Johanna in (7/4) hours is ?

(2+1)* (7/4) = 21/4 units of work is completed.

Johanna * t + (21/4) = 6

Johanna * t = 6-(21/4)

We know the efficiency of Johanna is 1.

Therefore, t = (3/4)

Converting into minutes = (3/4)*60 = 45 minutes.

Option C
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Lena can complete a certain task in 3 hours 16 Apr 2026, 02:57
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Not the author of the comment above, but Johanna completes her part of the work in 3/4 hr. She does not complete 3/4 units of work herself in the timeframe when she alone works.

Both of them complete 7/8th of the work, when working together. [ 7/4(1/3+1/6) = 7/8.]
Remaining 1/8th of work is done by Johanna alone. Equation:
1/8 = 1/6x
1/8th of work = Rate of Johanna * Time taken. Time taken is what is asked or x value i asked.
x = 3/4. Convert it into minutes you get 45 minutes.
SubaitaS
Could you pls explain the last part where you got 3/4*60 ? I got it till that part, Joanna finishes 3/4 units of the total work, but what you did there after that?

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