|
Question 1151536: Please help me solve this question: Machine A can do a piece of work in 6hrs while machine B can do the same work in 9hrs. Machine A and B was set to do the piece of work but after three and a half hours Machine A broke down. For how long machine B took to do the rest of the work
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A does the job in 6 hours.
B does the job in 9 hours.
r * t = q
r is the rate
t is the time
q is the quantity
in this problem q = 1 which represents one piece of work.
for machine A, the formula becomes r * 6 = 1
solve for r to get r = 1/6
for machine B, the formula becomes r * 9 = 1
solve for r to get r = 1/9
when they work together, their rates are additive.
the formula becomes (rA + rB) * t = q
they both work together for 3.5 hours.
the formula becomes (rA + rB) * 3.5 = q
since rA = 1/6 and rB = 1/9, the formula becomes (1/6 + 1/9) * 3.5 = q
solve for q to get q = (1/6 + 1/9) * 3.5 = (3/18 + 2/18) * 3.5 = 5/18 * 3.5 = 17.5/18 = 35/36.
when they worked together for 3.5 hours, they were able to complete 35/36 of the job.
that means that 1/36 of the job is left to do.
machine A broke down and machine B is left to finish the job.
formula for machine B to finish the job is equal to r * t = q which becomes 1/9 * t = 1/36
solve for t to get t = 9/36 hours = 1/4 hours = 15 minutes.
|
|
|
| |
