Question 1151536
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.