Question

A alone can do a piece of work in 7 days and B alone can do the work in 8 days. If both of
them work together, how long will they take to complete the work?​

Answer 1

Answer:

$3\frac{11}{15}$ days

Step-by-step explanation:

A can do the work in 7 days

=> In one day A can complete 1/7 of the work

B can do the work in 8 days

=> In one day B can complete 1/8 of the work

If A and B work together,

In one day they will complete (1/7) + (1/8) of the work

Fraction of work completed by (A + B) in 1 day = 1/7 + 1/8

                                                                             = 8/56 + 7/56

                                                                             = 15/56

If A+B can complete 15/56 of the work in 1 day,

A+B will take 56/15 days to complete the work

Time taken for A+B to complete the work = (56/15) days

                                                                      = 3.733 days

                                                                       = $3\frac{11}{15}$ days

A and B working together will take $3\frac{11}{15}$ days to complete the work

Remember:

If $\frac{1}{n}$ of the work is done in 1 day, it will take "n" days to complete the work.

This means:

Time taken to complete a work is the reciprocal of the fraction of work completed in one day.