SOLUTION: blueberry can do a certain job in 10 hours and cheescake can do it in 12 hours. after blueberry and cheesecake have been working together for 1 hour, Duhat joins them, and the thre

Algebra ->  Rate-of-work-word-problems -> SOLUTION: blueberry can do a certain job in 10 hours and cheescake can do it in 12 hours. after blueberry and cheesecake have been working together for 1 hour, Duhat joins them, and the thre      Log On


   

Question 1022901: blueberry can do a certain job in 10 hours and cheescake can do it in 12 hours. after blueberry and cheesecake have been working together for 1 hour, Duhat joins them, and the three completed the job in 3 more hours. How long will it take duhat to do the job alone?
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
PERSON                 RATES in JOBS/HOUR

blueberry                 1%2F10

cheesecake                1%2F12

blueberry&cheesecake     1%2F10%2B1%2F12=22%2F120=11%2F60

duhat                     1%2Fx


Work rates rule, RT=J relates rate, time, and amount of job or jobs.

The ONE job was split into two time parts, in 1 hour and 3 hour parts. Only one variable is unknown when the data formed into an equation.

highlight%28%2811%2F60%29%2A1%2B%2811%2F60%2B1%2Fx%29%2A3=1%29-----not the answer; but the equation which will contain the answer, once solved for x.


ALGEBRAIC SOLVING STEPS
60x%2811%2F60%29%2B60x%2811%2F60%2B1%2Fx%29%2A3=60x
11x%2B33x%2B60%2A3=60x
44x%2B180=60x
180=16x
45=4x
x=45%2F4
highlight%28x=11%261%2F4%29------hours for duhat to do one job alone.*


* Mistake fixed.