SOLUTION: I don't really understand word problems like this: Kate could do 10 jobs in 20 minutes and Ethan could do 15 jobs in 35 minutes. How long would it take both Kate and Ethan to do 3

Algebra ->  Rate-of-work-word-problems -> SOLUTION: I don't really understand word problems like this: Kate could do 10 jobs in 20 minutes and Ethan could do 15 jobs in 35 minutes. How long would it take both Kate and Ethan to do 3      Log On


   

Question 940919: I don't really understand word problems like this:
Kate could do 10 jobs in 20 minutes and Ethan could do 15 jobs in 35 minutes. How long would it take both Kate and Ethan to do 30 jobs?
Please help me the best way possible. Thank you!
Found 2 solutions by macston, MathLover1:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Kate could do 10 jobs in 20 minutes, so she does 10 jobs/20 min or 0.5 job per min. Ethan could do 15 jobs in 35 minutes so he does 15 jobs/35 min or 0.429 job per minute. Working together they would do (0.5+0.429)=0.929 job/min. To do 30 jobs at 0.929 job per minute:
Time=Jobs/rate=30/0.929=32.3 minutes

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if Kate could do 10 jobs in 20 minutes, then she could do at the rate +10jobs%2F20min=%281%2F2%29%28job%2Fmin%29

and if Ethan could do 15 jobs in 35 minutes, he could do at the rate +15jobs%2F35min=%283%2F7%29%28job%2Fmin%29
Let t=amount of time it takes them to do jobs working together.
Together, they could do jobs at the rate of 1%2F2%2B3%2F7=7%2F14%2B6%2F14=13%2F14
So our equation to solve is:
%2813%2F14%29t=30+....... multiply each side by 14
14%2813%2F14%29t=30%2A14+
13t=420+
t=420%2F13+
t=32.31min+
t=32min+and 18seconds would take both Kate and Ethan to do 30 jobs