Bunuel wrote:
Two workers A and B manufactured a batch of identical parts. A worked for 2 hours and B worked for 5 hours and they completed half the job. Then they worked together for another 3 hours and they had to do (1/20)th of the job. How many hours time does B take to complete the job, if he worked alone?
A. 12
B. 15
C. 18
D. 24
E. 30
Let T = the total job
Let A = Worker A's rate per hour
Let B = Worker B's rate per hour
A worked for 2 hours and B worked for 5 hours and they completed half the job.We can write:
2A + 5B = T/2Then they worked together for another 3 hours and they had to do (1/20)th of the job. In other words, after working together for three hours, 1/20 out the job (T) remained uncompleted.
1/2 - 1/20 = 9/20
So, the workers completed 9/20 of the job during those 3 hours.
We can write:
3A + 3B = 9T/20How many hours time does B take to complete the job, if he worked alone?We have:
2A + 5B = T/23A + 3B = 9T/20Let's first eliminate the fractions by multiplying both sides of the top equation by 2, and by multiplying both sides of the bottom equation by 20 to get:
4A + 10B = T60A + 60B = 9TSimplify the bottom equation by dividing both sides by 3:
4A + 10B = T20A + 20B = 3TMultiply both sides of the top equation by 5 to get:
20A + 50B = 5T20A + 20B = 3TSubtract the bottom equation from the top equation: 30B = 2T
Divide both sides by 2 to get:
15B = T
This tells us. It will take machine B
15 hours to complete the total job
Answer: B
Cheers,
Brent