Tired Brain needs math help

[LinRTX]

Ok since my pulled muscle in my back is preventing sleep, I cannot figure out how to do this math problem. Help please!

 

Problem:

Karen and Jessie work at a fast-food restaurant after school. Working alone, Jessie can close up in one hour less time than Karen. Together they can close up in 2/3 of an hour. How long does it take for Jesse to close up alone?

 

 

[regentrude]

This is a rate problem. Let us look at the rates at which the girls work. Rate is work per time, and let W be the work needed to close. All times in hours.

Joint rate: W/(2/3) or 3/2 W

Jessie's rate: W/t where t is Jessie's time in hours

Karen's rate: W/(t+1)

 

Rate of work * time worked=work done.

If they both work, the total work done W equals Jessie's rate * 2/3 hours + Karen's rate*2/3 hours:

W= (W/t)*2/3+(W/(t+1))*2/3

so 

1/t+1/(t+1)=3/2

Solve for t. It will become a quadratic equation.

t= 1 if I did not mess up the arithmetic

 

Jessie needs 1 hour working alone. Karen needs 2 hours working alone.

 

See that this makes sense:

Jessie works twice as fast as Karen. So having Karen help cuts her time to 2/3 of her original time.

If they both worked at the same rate, the joint time would be half.

 

 

 

Edited August 8, 2016 by regentrude

[LinRTX]

Thank you! I was trying something more complicated and messed up the simple math. I found my problem (once I looked at how you did it) and got the same answer finally.

 

This tired brain, for some reason, was dividing 6 by 3 and getting 3! But what I had was so complicated I could not find the simple math error!

 

Thanks again.