Question 269748
A new copying machine can do a certain job in 1 hour less than an older copier. Together they can do this job in 72 minutes. How long would it take the older copier by itself to do the job>
:
Change 72 min; 72/60 = 1.2 hrs
:
Let x = time for the older copier to do the job
then
(x-1) = time required by the new copier
:
Let the completed job = 1
:
Each copier will do a fraction of the job, the two factions add up to 1
{{{1.2/x}}} + {{{1.2/((x-1))}}} = 1
Multiply equation by x(x-1); results:
1.2(x-1) + 1.2x = x(x-1)
:
1.2x - 1.2 + 1.2x = x^2 - x
:
2.4x - 1.2 = x^2 - x
Arrange as a quadratic equation
x^2 - x - 2.4x + 1.2 = 0
x^2 - 3.4x + 1.2 = 0
Factors to
(x-3)(x-.4) = 0
Two solutions
x = 3 hrs is the reasonable answer for the older machine
:
:
check solution
1.2/3 + 1.2/2 =
.4 + .6 = 1