Question

Please help me, I'm having a hard time setting up this problem.
George can plant a garden in 2 hours, and it takes Joyce 3 hours. They work together for 45 mins, and George leaves and Joyce finishes the job alone. How long does it take Joyce to finish planting the garden?

Answer 1

job done = rate x time

George's rate = job/2
Joyce's rate = job/3
combined rate = job/2 + job/3 = 5job/6

let Joyce's time working alone be t hrs

(3/4) (5job/6) + t(job/3) = job
divide by job
(3/4)(5/6) + t/3 = 1
times 24
15 + 8t = 24
8t = 9
t = 9/8 hrs or (9/8)(60) minutes = 67.5 minutes
or 1 hour, 7.5 minutes