Question

By​ himself, a person can mow his lawn in 24 minutes. If his daughter​ helps, they can mow the lawn together in 20 minutes. How long would it take his daughter to mow the lawn by​ herself?

Answer 1

It would take 120 minutes to mow the lawn by herself.

Explanation:

The person's rate is
`(1 lawn)/(24 minutes) =(1)/(24)(lawn)/(minute)`.

The dauther's rate is
`(1 lawn)/(t)`.

The combined rate is
`(1lawn)/(20minutes)`.

So, as this the same lawn if we use the formula for combined rates we can get the answer

Person's Rate × Combined time + Daugther's Rate × Combined time =1

`(1)/(24)20minutes+(1)/(t) 20minutes=1`

We have to multiply all the equation by 24t:

20t+480=24t

t=120 minutes