Question 188348
Suppose that Arlene can mow the entire lawn in 40 minutes less time with the
 power mower than she can with the push mower.  One day the power mower broke
 down after she had been mowing for 30 minutes.  She finished the lawn with
 the push mower in 20 minutes.  How long does it take Arlene to mow the entire
  lawn with the power mower:
:
Let t = time required to mow the lawn with the power mower (in minutes)
then
(t+40) = time required with the push mower
:
Let the completed job = 1
;
{{{30/t}}} + {{{20/((t+40))}}} = 1
multiply equation by t(t+40) to get rid of the denominators, results:
30(t+40) + 20t = t(t+40)
:
30t + 1200 + 20t = t^2 + 40t
:
50t + 1200 = t^2 + 40t
:
0 = t^2 + 40t - 50t - 1200
A quadratic equation:
t^2 - 10t - 1200 = 0
Factors to:
(t - 40)(t + 30) = 0
Positive solution is what we want here:
t = 40 minutes to mow the lawn with power
;
:
Check solution:
{{{30/40}}} + {{{20/80}}} =
{{{3/4}}} + {{{1/4}}} = 1