SOLUTION: (GIVE THE ANSWER IN HOURS AND MINUTES) BILL CAN BUILT A BOOKCASE IN 6 HOURS, BUT IT TAKES HIS FRIEND, DAVID, ONLY 4 HOURS TO BUILD THE SAME BOOKCASE. HOW LONG WILL IT TAKE THEM TO

Algebra ->  Rate-of-work-word-problems -> SOLUTION: (GIVE THE ANSWER IN HOURS AND MINUTES) BILL CAN BUILT A BOOKCASE IN 6 HOURS, BUT IT TAKES HIS FRIEND, DAVID, ONLY 4 HOURS TO BUILD THE SAME BOOKCASE. HOW LONG WILL IT TAKE THEM TO      Log On


   

Question 170060: (GIVE THE ANSWER IN HOURS AND MINUTES)
BILL CAN BUILT A BOOKCASE IN 6 HOURS, BUT IT TAKES HIS FRIEND, DAVID, ONLY 4 HOURS TO BUILD THE SAME BOOKCASE. HOW LONG WILL IT TAKE THEM TO BUILD THE BOOKCASE IF THEY WORK TOGETHER?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes to build the bookcase when they both work together
So, together they work at the rate of 1/x bookcase per hour
Bill works at the rate of 1/6 bookcase per hour
David works at the rate of 1/4 bookcase per hour
Together they work at the rate of 1/6 + 1/4 =2/12 +3/12=
5/12 bookcase per hour
So our equation to solve is:
(5/12)x=1 (1 bookcase that is) multiply each side by 12
5x=12
x=12/5 = 2 2/5 hours (2/5 hour=(2/5)*60 min=24 min)
x=2h 24m
another way would be:
1/x = 5/12 multiply each side by 12x
12=5x-------same as before
CK
In 12/5 hr, Bill alone could build (12/5)*(1/6)=2/5 bookcase
In 12/5 hour David alone could build (12/5)*(1/4)=3/5 bookcase
Together they build 2/5 + 3/5 =1 bookcase
Hope this helps---ptaylor