A alone can reap a field in 15 days

Asked by admin @ 23/08/2021 in Math viewed by 433 People

A alone can reap a certain field in 15 days and b in 12 days. If a begins alone and after a certain interval b joins him the field is reaped in 712 days. How long did a and b work together?

Answered by admin @ 23/08/2021

A and B work together for 6 days.

Step-by-step explanation:

Consider the provided information.

It is given that A alone can reap a certain field in 15 days and b in 12 days.

Therefore, the work done of A for 1 day is $\frac{1}{15}$

The work done of B for 1 day is $\frac{1}{12}$

Work done of A and B for 1 day is $\frac{1}{15}+\frac{1}{12}=\frac{3}{20}$

a begins alone and after a certain interval b joins him the field is reaped in 7 1/2 days.

$7\frac{1}{2}=7.5$

Let A work of x days then they work together for 7.5-x days.

$\frac{3}{20}(7.5 - x) + \frac{1}{15} x= 1$

Multiply both side by 60.

$9(7.5 - x) +4x= 60$

$67.5 -9 x+4x= 60$

$-5x=-7.5$

$x=1.5$

They work together for 7.5-x days.

7.5-1.5=6

Hence, A and B work together for 6 days.

#Learn more

A man has some hens and some cows. if the number of feer 12:35, find out the numbers of hens , if number of head alone is 48.

a)24

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