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
Hello, Paul!
I'll do it the old-fashioned way . . .
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.