SOLUTION: Haileys father can paint a house 1.5 times faster then Hailey can. they work together on one house and it takes them 14 hours. How many hours will it take Hailey to paint a house

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Haileys father can paint a house 1.5 times faster then Hailey can. they work together on one house and it takes them 14 hours. How many hours will it take Hailey to paint a house      Log On


   

Question 1035313: Haileys father can paint a house 1.5 times faster then Hailey can. they work together on one house and it takes them 14 hours.
How many hours will it take Hailey to paint a house working alone
Found 3 solutions by josgarithmetic, ankor@dixie-net.com, ikleyn:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
This is the first analysis of the description for their rates of work:

PERSONS             RATE AS JOBS/HOURS
Father              1.5%2A%281%2Fx%29
Hailey               1%2Fx
Both Together        1%2F14


1.5%2Fx%2B1%2Fx=1%2F14

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Haileys father can paint a house 1.5 times faster then Hailey can.
they work together On one house and it takes them 14 hours.
how many hours will it take Hailey to paint a house working alone?
:
let t = time for Father to paint the house alone
then
1.5t = time for Hailey to do it
:
let the completed job = 1
14%2Ft + 14%2F%281.5t%29 = 1
multiply equation by 3t, cancel the denominators
3(14) + 2(14) = 3t
42 + 28 = 3t
70 = 3t
t = 3/70
t = 231%2F3 hrs for Father to paint the house
:
" how many hours will it take Hailey to paint a house working alone"
1.5 * 231%2F3 = 35 hrs for Hailey

Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
.
Haileys father can paint a house 1.5 times faster then Hailey can. they work together on one house and it takes them 14 hours.
How many hours will it take Hailey to paint a house working alone
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let r be the Haileys rate of work, measured in job-per-hour.
Then Haileys father's rate of work is 1.5*r, measured in job-per-hour.

Their combined rate of work (when they are working together) is r + 1.5r = 2.5r.

From the condition, 2.5r = 1%2F14.

Hence, r = 1%2F%282.5%2A14%29 = 1%2F35.

It means that it takes Haileys 35 hours to complete the job.

To solve this problem, you do not need to solve quadratic equations.