Question

A can do 1/3 of a work in 5 days and B can do 2/5 of the work in 10 days. In how many days can both A and B together do the work?.

Answer 1

9.375 days

Explanation:

Let d be the number of days the do 1 work(job). The speed A can do the job is (1/3)/(5)=1/3 × 1/5=1/15. The speed B can do the job is (2/5)/(10)=2/5 × 1/10=2/50=1/25. (These speeds have units work per 1 day)

So the amount of work done in d days for A is 1/15×d=d/15 and that same amount of days B does 1/25×d=d/25 work.

We are trying to figure out when they ddo 1 work together.

We need to solve

d/15+d/25=1

Multiply both sides by 75=least common multiple of 15 and 25.

75d/15+75d/25=75

Reducing:

5d+3d=75

Combine like terms:

8d=75

Divide both sides by 8:

d=75/8

d=9.375