Question

Phyllis can rake a lawn in 50 minutes, and Jane can do it in 40 minutes. If Phyllis rakes for 5 minutes before Jane joins her, how long will it take them to finish together?

http://www.slimber.com/index.php?image=math-problem-two.g149927

I don't know how to do the x-5 thing, how do I interpret the "five minutes before Jane joins her"?

Answer 1

Phyllis can do 1/50 of the job per minute so in x minutes she does x/50 of the job.
Jane can do 1/40 of the job per minute but she only works for x-5 minutes because Phyllis has a 5 minute head start so Jane does (x-5)/40 of the job.
Working together,they do 1 entire job so the equation is:
\[\frac{x}{50}+\frac{x-5}{40}=1\]

Answer 2

thanks so much! and plus heheh could you answer the question before too? YOU'RE AWESOME! totally a fan.

Answer 3

wait LOL sorry! i multiplied 200(x/50 + x-5/40=1) and got 200x/50 + 200x-1000/40=200. and then cancel out

4x+5x-1000=200

4x+5x=1200
9x=1200
x=133 1/3
????

Answer 4

\[200\times\frac{x}{50}+200\times\frac{x-5}{40}=200\times1\]
\[4x+5x-25=200\]
\[9x=225\]
\[x=25\]

Answer 5

where did 25 come from? cause 200 x 5 is 1000, and cross cancel with 40 would be 250.