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.
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.
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
To find out how long it will take for all three to complete the task, we can calculate their combined work rate.
Let's denote the work rate of the man as M, the work rate of the other man as N, and the work rate of the boy as B.
The man completes the task in 21 hours, so his work rate is 1/21 of the task per hour (1 task / 21 hours = 1/21 task per hour).
Similarly, the other man's work rate is 1/28 of the task per hour (1 task / 28 hours = 1/28 task per hour), and the boy's work rate is 1/48 of the task per hour (1 task / 48 hours = 1/48 task per hour).
To find their combined work rate, we add their individual work rates:
M + N + B = 1/21 + 1/28 + 1/48
To simplify this equation, we can find a common denominator:
M + N + B = (48 + 36 + 21) / (21 * 28 * 48)
Now we can calculate the combined work rate:
M + N + B = 105 / (21 * 28 * 48)
M + N + B = 105 / 28224
M + N + B ≈ 0.003723 task per hour
Now, we can find the time it will take for all three to do the task by taking the reciprocal of their combined work rate:
Time = 1 / (M + N + B)
Time = 1 / 0.003723
Time ≈ 268.39 hours
Therefore, it will take approximately 268.39 hours for all three to complete the task if they work together.
To find out how long it will take for all three individuals to complete the task when working together, we need to calculate their combined work rate.
Let's first calculate their individual work rates:
- The first man completes the task in 21 hours, so his work rate is 1 task per 21 hours (1/21).
- The second man completes the task in 28 hours, so his work rate is 1 task per 28 hours (1/28).
- The boy completes the task in 48 hours, so his work rate is 1 task per 48 hours (1/48).
Now, let's calculate their combined work rate by adding up their individual work rates:
1/21 + 1/28 + 1/48 = (4/84) + (3/84) + (7/336)
= 14/336 + 12/336 + 7/336
= 33/336
Therefore, the combined work rate of all three individuals is 33/336 tasks per hour.
To determine how long it will take them to complete the task together, we can calculate the reciprocal of their combined work rate:
1 / (33/336) = 336/33 = 10.18 hours (rounded to two decimal places)
Hence, it will take approximately 10.18 hours for all three individuals to complete the task if they work together.