SOLUTION: When John mows for one hour and Sally mows for one hour and 30 minutes, they complete the job of getting the lawn mowed. When Sally mows for 30 minutes and John mows for 1 hour an

Algebra ->  Rate-of-work-word-problems -> SOLUTION: When John mows for one hour and Sally mows for one hour and 30 minutes, they complete the job of getting the lawn mowed. When Sally mows for 30 minutes and John mows for 1 hour an      Log On


   

Question 709861: When John mows for one hour and Sally mows for one hour and 30 minutes, they complete the job of getting the lawn mowed. When Sally mows for 30 minutes and John mows for 1 hour and 40 minutes, they complete the job of getting the lawn mowed. How many hours would it take for Sally to mow the lawn by herself, and how many hours would it take John to mow the lawn by himself?
Define two variables, write a system of equations, and then solve. Help?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Two different worker arrangements described. Each represent doing one job of mowing the lawn.

j for john's rate, s for Sally's rate.

mower______________rate__________time__________________jobs
john_______________j_____________60____________________60j
sally______________s______________90___________________90s
Total: 60j+90s=1

mower______________rate______________time_______________jobs
john_________________j_____________60+40=100_________100j
sally________________s_______________30______________30s
Total: 100j+30s=1

In each situation, the two are completing 1 job, so the sum of jobs in each case is 1. All time quantities used here are in MINUTES.

System to solve then is:
60j%2B90s=1
100j%2B30s=1