Answer:
9.375 days
Step-by-step 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
