AAPL wrote:Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?
A. 22
B. 25
C. 28
D. 32
E. 56
We are given that machine A produces bolts at a uniform rate of 120 every 40 seconds. Thus, the rate of Machine A is 120/40 = 3 bolts/second.
We are also given that Machine B produces bolts at a uniform rate of 100 every 20 seconds. Thus, the rate of Machine B is 100/20 = 5 bolts/second.
We need to determine the time it will take to produce 200 bolts when the two machines run simultaneously.
To determine the time to produce 200 bolts, we can use the combined work formula:
Work by Machine A + Work by Machine B = 200 bolts (the total work completed).
Because both machines are working simultaneously, we can say that they both work together for t seconds. We now can express the individual work done by Machine A and by Machine B. We must remember that work = rate x time.
Work done by Machine A = 3t
Work done by Machine B = 5t
3t + 5t = 200
8t = 200
t = 200/8 = 25
Alternate Solution:
Since Machine A produces 120 bolts every 40 seconds, it will produce 60 bolts every 20 seconds. Combined with Machine B, the two machines will produce 100 + 60 = 160 bolts every 20 seconds. To find the time it will take the two machines to produce 200 bolts, we can set up a simple proportion: "160 bolts is to 20 seconds as 200 bolts is to t seconds"
160/20 = 200/t
t = (200 x 20)/160 = 25 seconds
Answer: B
