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 mow

Question 60965This question is from textbook Algebra for College Students
: 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 20minutes. How long does it take Arlene to mow the entire lawn the power mower? This question is from textbook Algebra for College Students

Answer by ankor@dixie-net.com(22740) (Show Source): 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 20minutes. How long does it take Arlene to mow the entire lawn the power mower?
:
Let the completed job = 1
Let t = time required to mow the lawn with power mower (minutes)
Let (t+40) = time required with a push mower
:
Using both mowers:
= 1
:
Eliminate denominators, mult equation by t(t+40), resulting in:
30(t+40) + 20t = t(t+40)
:
30t + 1200 + 20t = t^2 + 40t; mult what's in brackets
:
-t^2 + 30t + 20t - 40t + 1200 = 0; arrange as a quadratic eq on the left
:
-t^2 + 10t + 1200 = 0
:
t^2 - 10t - 1200 = 0; mult by -1 to get t^2 positive, easier to factor
:
(t-40)(t+30) = 0
:
Positive solution
t = +40 min for power mower to do the job
:
Check:
= 1
:
Did this make sense to you? Any questions?

RELATED QUESTIONS
Suppose that Arlene can mow the entire lawn in 40 minutes less time with the power mower... (answered by ankor@dixie-net.com)

A lawn can be mowed in 20 minutes less time with a riding mower than a push mower. After... (answered by josgarithmetic,MathTherapy)

I want to mow my lawn this summer but I need a new lawn mower. I can choose a riding... (answered by stanbon)

need help with this word problem: shelly can cut a lawn with a riding mower in 5 hours (answered by nerdybill)

a push mower can mow a large area for 6 hours where as a mower with a riding mower van... (answered by josmiceli)

Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to... (answered by josmiceli)

Shelly can cut a lawn with a riding mower in 4 hours less time than it takes William to... (answered by josgarithmetic)

When Mike uses a riding mower, it takes him 3 hours to mow his lawn. When he uses a push (answered by ewatrrr)