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

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
+ =
+ =
RELATED QUESTIONS
A man and a boy perform a task in 2 days. They completed one-half of the task with the... (answered by ankor@dixie-net.com)

Set up a system of three equations with three variables. A, B, and C complete a task in... (answered by richwmiller)

A, B, and C complete a task in 3 days. On the first day they do 1/3 of the task with A... (answered by richwmiller)

Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take... (answered by ikleyn)

A man can do a certain task in 21 hours, another man can do the task in 28 hours and a... (answered by richwmiller,Edwin McCravy)

one person can complete a task 8 hours sooner than another person. working together both (answered by josmiceli)

1.'A' works twice as fast as 'B'. If both of them together take 6 days to complete the... (answered by josmiceli,vvnrichards)

By working 8 hours per day, Marley's team can complete a task in 15 1/2 days. Bill's... (answered by Boreal,greenestamps)

A contract is to be completed in 56 days and 104 men were set to work, each working 8... (answered by josgarithmetic)