Need help with word problem

Question

Father is mowing the lawn, it takes him 80 minutes. His daughter helps him and it takes them 60 minutes. How long would it take the daughter to do it by herself?

Answer 1

Hi Richard, these work problems revolve around how much each can do in period of time. Here the period is one minute.

 

The father can do 1/80 of the work in one minute. Together, they can do 1/60 of the work in one minute. The daughter does 1/x, since we do not know how long it would take her.

 

Equation:

 

1/80 + 1/x = 1/60

 

Solve for x:

 

To solve this problem, we need to find the common denominator. A simple way to do this is to multiply the entire equation by: 80 * 60 * x.

 

(80 * 60 * x) * (1/80 + 1/x = 1/60)

 

This results in: 

 

(60 * x) + (80 * 60) = (80 * x)

 

Note: in the first term, the 80's cancel out, in the second term the x's cancel out, and on the right side of the equal sign, the 60's cancel out.

 

60x + 4800 = 80x

 

Subtract 60x from both sides of the equation giving:

 

4800 = 20x

 

Divide both sides by 20 giving x:

 

x = 240

 

Solution, it would take the daughter 240 minutes to do the work alone.

 

To check:

 

To check our answer, substitute 240 for the x and see if the values on both sides of the equal sign are the same.

 

Questions?

Answer 2

In 60 minutes the father does 60/80, or 3/4 of the lawn.

Therefore the daughter does 1/4 of the lawn in 60 minutes.

She would need four hours working alone.