Machine A produces bolts at a uniform rate…
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