Question

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 8 hours working together find how long to the nearest tenth of an hour it takes for William to cut the lawn alone. 13.9 hr 19.0 hr 18.9 hr 14.0 hr

Answer 1

Let time taken by william alone = x hour
then time taken by Shelly = (x-5) hour
So, part of work completed by Willian in 1 hour = 1/x
and, part of work completed by Shelly in 1 hour = 1/(x-5)
Total work completed in 1 hour if both work together = 1/x + 1/(x-5)

Together they finish work in 8 hours,
So,
In 1 hours together they finish 1/8 of work

Equate both:
1/x + 1/(x-5) = 1/8
((x-5)+x) / (x(x-5)) = 1/8
(2x-5) / (x^2-5x) = 1/8
16x - 40 = x^2 - 5x
x^2 - 21x + 40 = 0

This is quadratic equation (ax^2+bx+c=0)
a = 1
b = -21
c = 40

Roots can be found by
x = {-b + sqrt(b^2-4*a*c)}/2a
x = {-b - sqrt(b^2-4*a*c)}/2a

b^2-4*a*c = 2.81*10^2

roots are :
x = 18.9 and x = 2

x can't be 2 as this will make x-5 negative
x = 18.9
Answer: 18.9 days