SOLUTION: A man and a boy perform a task in 2 days. They completed one half of the task the first day with the man working 8 hours and the boy working 10 hours. On the next day, they finish

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Question 511281: A man and a boy perform a task in 2 days. They completed one half of the task the first day with the man working 8 hours and the boy working 10 hours.
On the next day, they finished the task with the man working 4 hours and the boy working 15 hours. Find how many hours would take for each to do the task working alone.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A man and a boy perform a task in 2 days.
They completed one half of the task the first day with the man working 8 hours and the boy working 10 hours.
On the next day, they finished the task with the man working 4 hours and the boy working 15 hours.
Find how many hours would take for each to do the task working alone.
:
Let m = time required by the man working alone
let b = time required by the boy working alone
Let the completed job = 1
:
1st day equation:
+ =
2nd day equation:
+ =
:
multiply the 2nd equation by 2, subtract the 1st equation
+ = 1
+ =
------------------- eliminates m, find b
=
b = 2(20)
b = 40 hrs, boy alone
:
Find m
+ =
reduce fraction
+ =
multiply by 4m
4(8) + m = 2m
32 = 2m - m
m = 32 hrs, man alone
:
:
Confirm this using the 2nd day equation
+ =
+ =