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

Answer:

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

Step-by-step explanation:

The person's rate is $\frac{1 lawn}{24 minutes} =\frac{1}{24}\frac{lawn}{minute}$.

The dauther's rate is $\frac{1 lawn}{t}$.

The combined rate is $\frac{1lawn}{20minutes}$.

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

$\frac{1}{24}20minutes+\frac{1}{t} 20minutes=1$

We have to multiply all the equation by 24t:

20t+480=24t

t=120 minutes