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August 23rd, 2019, 07:38 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 486 Thanks: 1  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? 
August 23rd, 2019, 08:13 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,110 Thanks: 2326 
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. 
August 26th, 2019, 07:31 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 486 Thanks: 1 
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"?

August 26th, 2019, 08:10 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 3,094 Thanks: 1677 
A's construction rate ... $\dfrac{\text{1 wall}}{\text{6 hrs}}$ B's destruction rate ... $\dfrac{\text{1 wall}}{\text{10 hrs}}$ $\left(\dfrac{\text{1 wall}}{\text{6 hrs}}  \dfrac{\text{1 wall}}{\text{10 hrs}}\right) \cdot \text{ (time in hrs) } = \text{ 1 wall built}$ $\dfrac{1}{15} \cdot t = 1$ $t = 15 \text{ hrs}$ 
August 26th, 2019, 11:43 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 21,110 Thanks: 2326  
August 26th, 2019, 09:40 PM  #6 
Senior Member Joined: Aug 2014 From: India Posts: 486 Thanks: 1  
August 26th, 2019, 11:12 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 21,110 Thanks: 2326 
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.

September 2nd, 2019, 11:05 PM  #8  
Senior Member Joined: Aug 2014 From: India Posts: 486 Thanks: 1  Quote:
Why multiply 26/2 with 2? How you got 48 mins? Last edited by Ganesh Ujwal; September 2nd, 2019 at 11:19 PM.  
September 3rd, 2019, 12:29 AM  #9 
Senior Member Joined: Apr 2014 From: UK Posts: 967 Thanks: 344  After 26 hours, each person has worked 26/2 hours 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 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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demolition, problem, time, work 
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