Question 644417
A and B can finish the job in 6 days.
 A can work 5 days less than B.
 Find the number of days it would take each working alone to finish the job.
:
Let a = time required by a working alone
then
(a+5) = time required by b working alone
Let the completed job = 1
:
{{{6/a}}} + {{{6/((a+5))}}} = 1
multiply by a(a+5)
a(a+5)*{{{6/a}}} + a(a+5)*{{{6/((a+5))}}} = a(a+5)
cancel out the denominators
6(a+5) + 6a = a(a+5)
6a + 30 + 6a = a^2 + 5a
combine on the right
0 = a^2 + 5a - 12a - 30
A quadratic equation
a^2 - 7a - 30 = 0
Factors to
(a-10)(a+3) = 0
The positive solution is all we want here
a = 10 hrs A's time working alone
then, obviously
B requires 15 hrs working alone