SOLUTION: Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 5 hours working together, find

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 5 hours working together, find       Log On


   

Question 196079: Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 5 hours working together, find how long to the nearst tenth of an hour, it takes for William to cut the lawn alone.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Their rates of mowing add to get their rate
working together
In words:
(number of lawns mowed by Shelly)/(time it takes Shelly to mow them) plus
(number of lawns mowed by William)/(time it takes William to mow them) equals
(number of lawns mowed by Shelly and william together)/(time to mow them)
Let Shelly's time to mow 1 lawn = t hrs
Then William's time = t+%2B+5 hrs
Time mowing together = 5 hrs
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1%2Ft+%2B+1%2F%28t%2B5%29+=+1%2F5
Multiply both sides by 5t%2A%28t+%2B+5%29
5%2A%28t+%2B+5%29+%2B+5t+=+t%2A%28t+%2B+5%29
5t+%2B+25+%2B+5t+=+t%5E2+%2B+5t
t%5E2+-+5t+=+25
Solve by completing the square:
t%5E2+-+5t+%2B+%285%2F2%29%5E2+=+25+%2B+%285%2F2%29%5E2
t%5E2+-+5t+%2B+25%2F4+=+100%2F4+%2B+25%2F4
%28t+-+5%2F2%29%5E2+=+125%2F4
Take the square root of both sides
t+-+5%2F2+=+5%2Asqrt%285%29%2F2
t+=+5%2A%281+%2B+sqrt%285%29%29%2F2
t+=+8.090 hrs
t+%2B+5+=+13.090 hrs
William's time mowing alone is 13.1 hrs
check answer:
1%2Ft+%2B+1%2F%28t%2B5%29+=+1%2F5
1%2F8.09+%2B+1%2F13.09+=+1%2F5
.1236+%2B+.0764+=+.2
.199994+=+.2 close enough