Question

Really need help with this one!
Thanks!!!

Jay and Raul are raking leaves to earn some money. Jay can rake 3 lawns that are about the same size in 4 hours. Raul can rake 3 lawns that are about the same in 5 hours. How long would it take both boys to work together to rake 3 lawns? Write and solve an equation for this situation. Explain how to set up the equation, using w = rt.

Answer 1

Okay, what you want to do in these problems is figure out the unit rate: how fast does each resource work, by itself. Jay can rake 3 lawns in 4 hours, so his rate \(R_j\) is \(3/4\). Raul can rake 3 lawns in 5 hours, so his rate \(R_r\) is \(3/5\). Does that make sense? In other words, in 1 hour, Jay can rake \[w = rt\]\(w = 3/4* 1 = 3/4\) of a lawn, and Raul can do \(3/5\) of a lawn by the similar calculation. Together, they rake \(R_{total}=R_j+R_r = 3/4+3/5\) lawns per hour. Use that to find how long it will take them to rake the 3 lawns.

Answer 2

Thanks!!! You explained it very well!

Answer 3

Tell me your answer, and we'll find out if I really explained it well :-)

Answer 4

J = 3/4 lawns/hour
R = 3/5 hours/lawn

J+R = 3/4 + 3/5 = 27/20 lawns/hour

Togethere Jay and Raul takes 20/27 hours to rake 1 lawn or 60/27 = 20/9 = 2 1/3 hours = 2 hours 20 minutes to rake 3 lawns.

Answer 5

Ooh, close...you got the right answer, but the conversion to time was incorrect...

20/9 = 2 2/9, so that's 2 hours + 2*60/9 minutes or 2 hours 40/3 minutes or 2 hours 13.3333 minutes

Answer 6

Ohhhh, I see that. Thanks!

Answer 7

All these "filling swimming pools", "mowing lawns", "draining tanks", etc. problems boil down to finding the rates at which each item works.

Answer 8

and usually some messy work with fractions :-)