SOLUTION: 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 mo
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-> SOLUTION: 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 mo
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Question 188348This question is from textbook
: 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? This question is from textbook
You can put this solution on YOUR website! 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
; + = 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: + = + = 1
