Time and Work Basic Examples
In this class, We discuss Time and Work Basic Examples.
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Before going to examples we understand few important points.
A’s one day work = 1/8
B’s one day work = 1/7
A and B work together Then (A + B)’s one day work = (1/8 + 1/7)
Example 1:
Worker A takes 8 hours to do a job and worker B takes 10 hours to do the same job.
How long will it take both A and B work together to do the same job?
Solution:
A can do a work in 8 hours.
A’s one hour work = 1/8
B can do a work in 10 hours.
B’s one hour work = 1/10
(A + B)’s one hour work = (1/8 + 1/10) = 9/40
(A + B) can finish the work in 40/9 hours = 4 4/9 hours
From the Formulae: A’s one hour work is 1/n then A can finish work in n hours.
Example 2:
A and B together can complete a piece of work in 4 days.
A alone can finish the work in 12 days. In how many days B alone can complete the work?
Solution:
(A + B)’s one day work = 1/4
A’s one day work = 1/12
B’s one day work = A + B = 1/4
1/12 + B = 1/4
B = 1/4 – 1/12
B = 1/6
So B can finish the work in 6 days.
Example 3:
A can do a peice of work in 7 days of 9 hours each.
B can do the same work in 6 days of 7 hours each.
How long will they take to do it working together 8 2/5 hours a day?
Solution:
Important: Each day number of hours are different for A and B.
So we convert to hours.
A’s working hours = 7 * 9 = 63 hours
B’s working hours = 6 * 7 = 42 hours
A’s one hour work = 1/63
B’s one hour work = 1/42
(A + B)’s one hour work = ( 1/63 + 1/42) = 5/126
A+B can finish the work in 126/5 hours.
Number of days = (126/5)/8 2/5
= (126/5)/42/5
= 3 days.