# [SOLVED] Twist on Work Rate Problem

• Mar 19th 2007, 07:41 PM
Paul B
[SOLVED] Twist on Work Rate Problem
I am trying to show my students a different slant on a work rate problem and I want to make sure I show them the best method.

Working together, Nina and Lauren can mow the lawn in 2 hours. It takes Nina 3/4 as long as Lauren to do the job alone. How long would it take Nina working alone?

I appreciate the help. My applied Algebra kids struggle with these.

Paul:)
• Mar 19th 2007, 07:52 PM
ThePerfectHacker
Quote:

Originally Posted by Paul B
I am trying to show my students a different slant on a work rate problem and I want to make sure I show them the best method.

Working together, Nina and Lauren can mow the lawn in 2 hours. It takes Nina 3/4 as long as Lauren to do the job alone. How long would it take Nina working alone?

I appreciate the help. My applied Algebra kids struggle with these.

Paul:)

I use a formula I developed.

If "a" and "b" are the times one person completes a job and another completes a hour (say in hours).

Then working together it takes,
(ab)/(a+b)
Hours.

Thus,
(NL)/(N+L)=2

And

N=L+3/4

Now use this system.
• Mar 19th 2007, 08:37 PM
Soroban
Hello, Paul!

I'll do it the old-fashioned way . . .

Quote:

Working together, Nina and Lauren can mow the lawn in 2 hours.
It takes Nina ¾ as long as Lauren to do the job alone.
How long would it take Nina working alone?

Let N = number of hours for Nina to mow the lawn alone.
Let L = number of hours for Lauren to mow the lawn alone.

In one hour, Nina can mow 1/N of the lawn.
In one hour, Lauren can mow 1/L of the lawn.

Together, it takes them 2 hours to mow the lawn.
So in one hour, they can mow ½ of the lawn.

We have: .1/N + 1/L .= .1/2 . . 2L + 2N .= .LN . [1]

We are told that: .N = ¾L

Substitute into [1]: .2L + 2(¾L) .= .L(¾L)

Multiply by 4/L: .8 + 6 .= .3L . . L = 14/3

Then: .N .= .(3/4)(14/3) .= .7/2

Therefore, working alone, Nine will take 3½ hours.