SOLUTION: A roofer requires 14 h to shingle a roof. After the roofer and an apprentice work on a roof for 7 h, the roofer moves on to another job. The apprentice requires 7 more hours to fin

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A roofer requires 14 h to shingle a roof. After the roofer and an apprentice work on a roof for 7 h, the roofer moves on to another job. The apprentice requires 7 more hours to fin      Log On


   

Question 812523: A roofer requires 14 h to shingle a roof. After the roofer and an apprentice work on a roof for 7 h, the roofer moves on to another job. The apprentice requires 7 more hours to finish the job. How long would it take the apprentice, working alone, to do the job?
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
rate = time/job
time = rate * job
job = time/rate
---
r = roofer work rate
a = apprentice work rate
---
r = 14 hr/job
---
use equation:
job = time/rate
---
7/(r + a) + 7/a = 1 job
7/(14 + a) + 7/a = 1 job
7a/(a(14 + a)) + 7(14 + a)/(a(14 + a)) = 1 job
7a/(aa + 14a) + 7(14 + a)/(aa + 14a) = 1 job
7a/(aa + 14a) + (7a + 98)/(aa + 14a) = 1 job
(14a + 98)/(aa + 14a) = 1 job
14a + 98 = aa + 14a
14a + 98 = aa + 14a
aa = 98
a = sqrt(98)
a ~= 9.8995 hr/job
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Convert fractions, decimals, and percents:
https://sooeet.com/math/fraction-decimal-percent.php
---
Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php