R alone can do a work in 6 days working 5 hours a day. S alone can do the same work in 4 days working 8 hours a day. How many hours do they need to work together in a day to complete the same work in 3 days?
Show answer & explanation
Correct answer: A
Explanation
Given:
R: 5 hours/day, 6 days ⇒ Total work = 30 hours
S: 8 hours/day, 4 days ⇒ Total work = 32 hours
R's rate = 1/30
S's rate = 1/32
Combined rate = 1/30 + 1/32
= (32 + 30) / 960
= 62 / 960
= 31 / 480
Let's assume they work *x* hours per day; the work will be completed in 3 days:
3 × x × (31/480) = 1
x = 480 / (31 × 3)
= 480 / 93 = 160/31 hours