SOLUTION: Working together, two people can mow a large lawn in 4 hours. One person can do the job alone 1 hour faster than the other person. How long does it take each person working alone t

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Question 404912: Working together, two people can mow a large lawn in 4 hours. One person can do the job alone 1 hour faster than the other person. How long does it take each person working alone to mow the lawn?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Working together, two people can mow a large lawn in 4 hours.
One person can do the job alone 1 hour faster than the other person.
How long does it take each person working alone to mow the lawn?
:
let t = time required by the faster person
then
(t+1) = time required by the other person
:
Let the completed job = 1
:
each man will do a fraction of the work, the two fractions add up to 1
:
4%2Ft + 4%2F%28%28t%2B1%29%29 = 1
:
Multiply by t(t+1) to clear the denominators, results:
4(t+1) + 4t = t(t+1)
:
4t + 4 + 4t = t^2 + t
:
8t + 4 = t^2 + t
:
0 = t^2 + t - 8t - 4
:
t^2 - 7t - 4 = 0
we have to use the quadratic formula to solve this
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem x=t, a = 1, b= -7, c = -4
t+=+%28-%28-7%29+%2B-+sqrt%28-7%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29+
t+=+%28%2B7+%2B-+sqrt%2849+%2B+16+%29%29%2F2+
t+=+%28%2B7+%2B-+sqrt%2865+%29%29%2F2+
Two solutions, only want the positive solution
t+=+%28%2B7+%2B+8.06%29%2F2+
t = 15.06%2F2
t = 7.53 hrs for the faster man to do the joy
and 8.53 hrs for the slower man
:
:
Check solution
4/7.53 + 4/8.53
5.31 + .469 = 1; confirms our solutions of 7.53 and 8.53 hr