Question

A man can do a certain task in 21 hours, another man can do the task in 28 hours and a boy can do the task in 48 hours. Find how long it will take to do the task if all three work.

Answer 1

Try figuring out how much of the task each man can do in one hour, as a fraction.

You can use that to find out the work done in an hour if all three work together, and thus the amount of time it will take.

Answer 2

Man 1/21 other man 1/28 boy 1/48
Man’s rate other man’s rate boy’s rate
1/21 1/28 1/48
Let x be the number of hours it will take all three
to do the task.
Combined rate = 1/x
1/21 + 1/28 + 1/48 =
LCD = 28, 224
1344 / 28, 224 + 1008 / 28, 224 + 588 / 28, 224
= 2 940 / 28, 224 or 735 / 7056
1/x = 735/7056
Cross multiply
735x = 7056
x = 7056/735
x = 9.6 or 9 hours and 10 minutes