Question 672824
A and B do a work together in five days
 If A do the work with double speed and
 B with half the speed then they do the work in 4 days together
 find A alone do the work in how much time.
:
let a = A's time alone
let b = B's time alone
then
.5a = A's time when working twice as fast
and
2b = B's time when working half as fast
:
Let the completed job = 1
:
Write a shared work equation for each scenario
:
{{{5/a}}} + {{{5/b}}} = 1
get rid of the denominators, mult by ab
5b + 5a = ab
and
{{{4/(.5a)}}} + {{{4/(2b)}}} = 1
multiply by 2ab to get rid of the denominators
4b(4) + 4a = 2ab
16b + 4a = 2ab
:
Use elimination here, mult the 1st equation by 4, mult the 2nd eq by 5
then subtract the 1st from the 2nd
80b + 20a = 10ab
20b + 20a = 4ab
------------------subtraction eliminates a
60b + 0 = 6ab
divide both sides by b
60 = 6a
a = 60/6
a = 10 days working alone