SOLUTION: Bob takes 3 hours to mow a lawn. Al takes 4 hours. If they work together how long will it take In the previous problem Al works for 1.5 hours BEFORE Bob arrives, how much longer

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Bob takes 3 hours to mow a lawn. Al takes 4 hours. If they work together how long will it take In the previous problem Al works for 1.5 hours BEFORE Bob arrives, how much longer      Log On


   

Question 999272: Bob takes 3 hours to mow a lawn. Al takes 4 hours. If they work together how long will it take
In the previous problem Al works for 1.5 hours BEFORE Bob arrives, how much longer will it
take if they finish together?
The answer for the first problem is 12/7 hrs. I'd like to know how to work out the second please!
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
The current problem works this way:
Bob's rate, 1%2F3.
Al's rate, 1%2F4.
Both together, 1%2F3%2B1%2F4=4%2F12%2B3%2F12=highlight%287%2F12%29. The unit is LAWNS per HOUR.
....Yes, you can look at that rate upside down to figure how much TIME for one job and this is 12%2F7 HOURS per job. Twelve hours for seven jobs or, 1%265%2F7 hours for one job or however you want to express it.




The "previous" problem works this way:
Al works 1%261%2F2 hours, and does some work; and then Al and Bob work together for some unknown t hours and they finish the 1 job.
-
highlight_green%28%281%2F4%29%283%2F2%29%2B%287%2F12%29%2At=1%29.
Solve this for t.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Al takes 4 hours to complete the job
so he does 1/4 of the job in hour
He worked 1.5 hours earlier
so he completed 1/4 * 1.5 = 3/8 of the job before Bob started
Balance job = 1-3/8 = 5/8
Together they doe 7/12 of the job in 1 hour
So to complete 5/8 of the job they take
%285%2F8%29%2F%287%2F12%29 hours
= 5/8 * 12/7 = 15/14 hours
15/14 + 3/2 = 36/14 = 18/7 hours