SOLUTION: A lawn can be mowed in 20 minutes less time with a riding mower than a push mower. After using riding mower for 15 minutes, it had mechanical problems and using push mower, the tas

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Question 1168201: A lawn can be mowed in 20 minutes less time with a riding mower than a push mower. After using riding mower for 15 minutes, it had mechanical problems and using push mower, the task took 25 more minutes to complete. Determine time (minutes) to mow entire lawn with riding mower.
Unsure how to proceed.


Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
        mow speed
rider   1%2F%28p-20%29
pusher  1%2Fp


15%2F%28p-20%29%2B25%2Fp=1-------for the one whole lawn

Solve for p and subtract 20.


Check to be sure you understand how that was set up.
If you do the algebra steps right, you may find an equation
p%5E2-60p%2B500=0
which is factorable as
%28p-10%29%28p-50%29=0

The solution which works is highlight%28p=50%29, the time for the push motor to do the job alone; and then p-20=highlight%2830%29, the time for the rider mower to do the job alone.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A lawn can be mowed in 20 minutes less time with a riding mower than a push mower. After using riding mower for 15 minutes, it had mechanical problems and using push mower, the task took 25 more minutes to complete. Determine time (minutes) to mow entire lawn with riding mower.
Unsure how to proceed.
Let time riding mower takes be T

Then time push mower takes = T + 20

We then get the following JOB equation: matrix%281%2C3%2C+15%281%2FT%29+%2B+25%281%2F%28T+%2B+20%29%29%2C+%22=%22%2C+1%29

matrix%281%2C3%2C+15%2FT+%2B+25%2F%28T+%2B+20%29%2C+%22=%22%2C+1%29

15(T + 20) + 25T = T(T + 20) ------ Multiplying by LCD, T(T + 20)



(T - 30)(T + 10) = 0

T - 30 = 0             OR                   T + 10 = 0

Time riding mower takes, or highlight_green%28matrix%281%2C4%2C+T%2C+%22=%22%2C+30%2C+minutes%29%29          OR         T = - 10 (ignore)