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August 23rd, 2019, 07:38 AM   #1
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Demolition in Time & Work problem.

A can build a wall in 6 hours, while B can demolish the same wall in 10 hours. In how many hours would A be able to build the wall if they work on alternate hours??

My attempt: total work 30 units

A's efficiency = 5

B efficiency = - 3
--------------------------------------
Combining gives me: 2 hours = 2 Units.

After this how to proceed?
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August 23rd, 2019, 08:13 AM   #2
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In 26 hours, 13 × 2 = 26 of the 30 units have been completed.

In the next 4/5 of an hour A completes the remaining (4/5)5 units = 4 units.

In total, A will have worked 13 4/5 hours, and B will have worked 13 hours.
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August 26th, 2019, 07:31 AM   #3
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Here B is destroying right after A. So there is no way to possible to build completely then how can we answer the question: "how many hours would A be able to build the wall"?
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August 26th, 2019, 08:10 AM   #4
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A's construction rate ... $\dfrac{\text{1 wall}}{\text{6 hrs}}$

B's destruction rate ... $\dfrac{\text{1 wall}}{\text{10 hrs}}$

$\left(\dfrac{\text{1 wall}}{\text{6 hrs}} - \dfrac{\text{1 wall}}{\text{10 hrs}}\right) \cdot \text{ (time in hrs) } = \text{ 1 wall built}$

$\dfrac{1}{15} \cdot t = 1$

$t = 15 \text{ hrs}$
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August 26th, 2019, 11:43 AM   #5
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Quote:
Originally Posted by Ganesh Ujwal View Post
Here B is destroying right after A.
Yes, but the question doesn't say the wall remains built. The wall is fully built for the first time after A has worked for 13 4/5 hours. That is the intended answer.
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August 26th, 2019, 09:40 PM   #6
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Quote:
Originally Posted by skipjack View Post
In 26 hours, 13 × 2 = 26 of the 30 units have been completed.
How you got this numbers: 13, 2 ?
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August 26th, 2019, 11:12 PM   #7
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In each pair of hours of the 26 hours, A completes 5 units of the wall and B then destroys 3 units, so that 2 units remain completed, so (26/2) × 2 units remain completed after 13 pairs of hours. It's then possible for A to complete the wall in just 48 minutes.
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September 2nd, 2019, 11:05 PM   #8
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Quote:
Originally Posted by skipjack View Post
so (26/2) × 2 units remain completed after 13 pairs of hours. It's then possible for A to complete the wall in just 48 minutes.
Why dividing 26 by 2?

Why multiply 26/2 with 2?

How you got 48 mins?

Last edited by Ganesh Ujwal; September 2nd, 2019 at 11:19 PM.
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September 3rd, 2019, 12:29 AM   #9
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Quote:
Originally Posted by Ganesh Ujwal View Post
Why dividing 26 by 2?
After 26 hours, each person has worked 26/2 hours

Quote:
Originally Posted by Ganesh Ujwal View Post
Why multiply 26/2 with 2?
after 26 hours, each pair of hours (there are 26/2 of them) results in 2 units of wall progress, so (26/2) x 2

Quote:
Originally Posted by Ganesh Ujwal View Post
How you got 48 mins?
at the start of the 27th hour, there are 4 units of wall to complete, but the builder can complete 5 units of wall in an hour, so it takes 4/5 of an hour to complete the remaining units of wall, this is 48 minutes.
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