SOLUTION: A carpenter can build 15 toolsheds three times as fast as his apprentice. Working together,they can build the sheds in 57 hours. How long would it take each of then working alone t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A carpenter can build 15 toolsheds three times as fast as his apprentice. Working together,they can build the sheds in 57 hours. How long would it take each of then working alone t      Log On


   

Question 825103: A carpenter can build 15 toolsheds three times as fast as his apprentice. Working together,they can build the sheds in 57 hours. How long would it take each of then working alone to build the sheds?

Found 2 solutions by TimothyLamb, josgarithmetic:
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
---
rates:
x = boss
y = worker
---
x = 15/t
y = 15/3t
y = 5/t
---
x + y = 15/57
15/t + 5/t = 15/57
20/t = 15/57
t = 20*(57/15)
t = 76 hr
---
x = boss = 76 hr
y = worker = 228 hr
---
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Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the time for the carpenter to build 15 sheds.

Rates are these, in sheds per hour.
Carpenter, 15%2Fx
Apprentice, 15%2F%283x%29
Both together, 15%2F57

You must solve for x to compute each individual rate.
highlight_green%2815%2Fx%2B15%2F%283x%29=15%2F57%29
1%2Fx%2B1%2F%283x%29=1%2F57
1%2B1%2F3=x%2F57
57%284%2F3%29=x
x=19%2A4
highlight%28x=76%29 hours

Use x.