Question

Gardener A can mow an entire lawn in 1 hour less time than Gardener B. If they work together, they can mow the lawn in 20/9 hours. How many hours will it take Gardener A to mow the lawn alone?

Answer 1

Gardner B takes 5 hr
Gardner A takes 4 hr.

Answer 2

Let x =gardener A time in hours
then x-1= gardener B time in hours.
when working together they accomplished the mowing in 20/9 hours
using the product over sum method:
\[x(x-1)\over 2x-1\]=20/9
cross multiplying:
9x(x-1)=40x-20
\[9x ^{2}-49x+20=0\]
use quadratic formula getting x=5, x=4

Answer 3

verify: product over sum
5(4) 20
---- = ----
5+4 9

Answer 4

Could of also used the reciprocal of the sums of reciprocal.

Answer 5

1 20
----------------------------- = ----
1 1 9
-------- + ---------
x x-1

This too will work out to be the same quadratic equation as above and the same answer.

Answer 6

Any questions?

Answer 7

thanks radar!

Answer 8

u r welcome