SOLUTION: Person A can paint the neighbors house 2 times as fast as person B. The year A and B worked together, it took them 6 days. how long would it take each to paint the house?

Question 805262: Person A can paint the neighbors house 2 times as fast as person B. The year A and B worked together, it took them 6 days. how long would it take each to paint the house?
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Look at rates according to jobs per time. "Paint the house" is the one job and time is in number of days.

Given an amount of days, d, agent A works at the rate of 1/d jobs per day and agent B works at the slower rate of 1/(2d) jobs per day.

When agents A and B work at the same time, the needed time for 1 job is 6 days.

r = rate
t = time in days
j = how many jobs.

This rate for A and B together is .
We are given the time for their one job, .
We understand that for 1 job.

The rate is what is unknown because the rate contains variable d, which is what we must solve for.

Solving for d should be uncomplicated. The rate for each of A and B can be computed using d.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Person A can paint the neighbors house 2 times as fast as person B.
The year A and B worked together, it took them 6 days. how long would it take each to paint the house?
Let a = A's time to paint the house
then
2a = B's time to do it
:
Let the completed job = 1; (a painted house):
Each will do a fraction of the job, the two fractions add up to one.
+ = 1
multiply by 2a, cancel the denominators
2(6) + 6 = 2a
18 = 2a
a = 9 days for A working alone
then
2(9) = 18 days for B to do it.
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