EgmatQuantExpert wrote:
When working independently, machine A can complete a piece of work in 10 hours, and machine B can complete the same wok in 6 hours. Both machines worked together for 3 hours, and then Machine A stopped working. How much more time did machine B take to complete the remaining work ?
A. 1 hour
B. 1 hours 12 minutes
C. 1 hour 20 minutes
D. 1 hour 48 minutes
E. 2 hours
Machine A’s rate is 1/10, and machine A worked for 3 hours. Machine B’s rate is 1/6. If we let n = the extra time that machine B worked, then machine B worked for (3 + n) hours. We can create the equation:
(1/10)(3) + (1/6)(3 + n) = 1
3/10 + (3+n)/6 = 1
Multiplying by 30, we have:
9 + 15 + 5n = 30
5n = 6
n = 6/5 = 1 1/5 = 1 hour and 12 minutes.
Alternate Solution:
Working alone, Machine A and Machine B can complete 1/10 and 1/6 of the job in one hour, respectively. Together, they complete 1/10 + 1/6 = 16/60 = 4/15 of the job in one hour. Since they work for 3 hours, 3 x 3/15 = 12/15 = 4/5 of the job is completed and 1 - 4/5 = 1/5 of the job remains. Since Machine B completes the whole job in 6 hours, it will complete 1/5 of the job in 6 x 1/5 = 6/5 hours or, equivalently, 1 hour and 12 minutes.
Answer: B
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