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

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) (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
:
+ = 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

In this problem x=t, a = 1, b= -7, c = -4

Two solutions, only want the positive solution

t =
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
RELATED QUESTIONS
Working together two people can cut a large lawn in 3 hours one person can do the job... (answered by stanbon)

Working together, two people can cut a large lawn in 5 hr. One person can do the job... (answered by JulietG)

Working together, two people can cut a large lawn in 5 hr. One person can do the... (answered by josmiceli)

working together , two people can cut a large lawn in 5 hours. One person can do the job... (answered by lwsshak3,mananth)

Working together, two people can cut out a large lawn in 2 hr. One person can do the job... (answered by josgarithmetic)

Hi, I need help on my word problem homework. Would someone kindly help me please.Please... (answered by josgarithmetic)

Working together, two people can complete a task in 10 hours. Working alone, one person... (answered by scott8148)

Suppose one person can mow a lawn in x hours and a second person can mow the same lawn in (answered by richwmiller)

Together, Diane and Craig can mow their lawN in 1 hour and 10 minutes. Working alone,... (answered by josgarithmetic,josh_jordan)