SOLUTION: Brett usually takes 50 minutes to groom the horses. After working 10 minutes, he was joined by Angela and they finished the grooming in 15 minutes. How long would it have taken Ang

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Brett usually takes 50 minutes to groom the horses. After working 10 minutes, he was joined by Angela and they finished the grooming in 15 minutes. How long would it have taken Ang      Log On


   

Question 132051: Brett usually takes 50 minutes to groom the horses. After working 10 minutes, he was joined by Angela and they finished the grooming in 15 minutes. How long would it have taken Angela working alone? Please explain the steps and the equation used. Thanks.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = Angela's time working alone
Add the rates at which each works to
get the rate of working together:
Note that if Brett can groom the horses in 50 min, and he works
alone for 10 min, he does 1/5 of the job, leaving 4/5 to be done
by both working together
(1 horse-grooming job)/(Angela's tme) + (1 horse-grooming job)/(Brett's time) =
(4/5 horse-grooming job done)/(time working together)
1%2F50+%2B+1%2Fx+=+%281+-+%281%2F5%29%29%2F+15
1%2F50+%2B+1%2Fx+=+%284%2F5%29%2F15
multiply both sides by 15%2A50%2Ax
15x+%2B+15%2A50+=+%284%2F5%29%2A50%2Ax
15x+%2B+750+=+40x
25x+=+750
x+=+30
It would take Angela 30 min working alone
check:
1%2F50+%2B+1%2Fx+=+%284%2F5%29%2F15
1%2F50+%2B+1%2F30+=+%284%2F5%29%2F15
multiply both sides by 30%2A50
30+%2B+50+=+%284%2F5%29%2830%2A50%29%2F15
80+=+%284%2F5%29%28100%29
80+=+80
OK