SOLUTION: B1 and B2 can solve a math problem together in 8 minutes. If B1 works alone for 3 minutes and is then joined by B2, the two together can solve the problem in 6 more minutes. How lo

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: B1 and B2 can solve a math problem together in 8 minutes. If B1 works alone for 3 minutes and is then joined by B2, the two together can solve the problem in 6 more minutes. How lo      Log On


   

Question 872709: B1 and B2 can solve a math problem together in 8 minutes. If B1 works alone for 3 minutes and is then joined by B2, the two together can solve the problem in 6 more minutes. How long will it take B1 and B2 alone to solve the problem?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This is a uniform rates doing-a-job type proglem. The sum of the job parts done is the whole job done.

Let x = the time in minutes for B1 alone to solve the problems. His work rate is 1/x.

highlight_green%28%281%2Fx%29%2A3%2B%281%2F8%296=1%29; You can use x to help find the rate for B2, because once x is found from the first shown equation, it will no longer be unknown, and you will be able to use: B1_and_B2_Combined=B1+B2, and the units used will be jobs per minute. Reminder is their combined rate is 1%2F8 jobs per minute.


USING THAT DESCRIPTION DISCUSSION AND THEN CONTINUE TO FINISH---------------------
LCD, 8x.
24%2B6x=8x
24=2x
x=12 twelve minutes, rate for B1 is highlight%281%2F12%29 jobs per minute.

Combined rate is known, and now B1 rate is known, so we can relate the sum of their rates:
1%2F12%2B1%2Fb=1%2F8, using b as the time for B2 to do the job alone.
LCD is 24b.
24b%2F12%2B24b%2Fb=24b%2F8
2b%2B24=3b
b=24 minutes for B2 to do the job alone.
Rate for B2 is highlight%281%2F24%29 jobs per minute.