Question

Carl and Bob can demolish a building in 6 days, Anne and Bob can do it in 3, Anne and Carl in 5. How many days does it take all of them working together if Carl gets injured at the end of the first day and can't come back ?​

Answer 1

• 59/20 days or 2.95 days

Explanation:

Let Carl do the job in c days, Anne- in a, and Bob in b days

Then the portion of job they can do is 1/c, 1/a and 1/b

As per given we have below equations:

• 1/c + 1/b= 1/6
• 1/a + 1/b = 1/3
• 1/a + 1/c = 1/5

Sum of all 3 equations gives us:

• 2(1/a + 1/b + 1/c) = 1/6 + 1/3 + 1/5
• 2(1/a + 1/b + 1/c) = 5/30 + 10/30 + 6/30
• 2(1/a + 1/b + 1/c) = 21/30
• 2(1/a + 1/b + 1/c) = 7/10
• 1/a + 1/b + 1/c = 7/20

It means all three together can complete 7/20 of the job in one day

The rest of the job is done by Anne and Bob:

• 1 - 7/20 = 13/20

As Anne and Bob can do 1/3 of the job in one day, they need time to complete the rest:

• 13/20:1/3 = 39/20

Add 1 day to this to find overall time:

• 1 + 39 /20 = 59/20 days or 2.95 days