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.