Machine A produces bolts at a uniform rate of 120 every 40

Machine A produces 120 bolts every 40 seconds.
How many bolts does Machine A produce every second?
Machine A produces 120/40 = 3 bolts every second.

Machine B produces 100 bolts every 20 seconds.
How many bolts does Machine B produce every second?
Machine B produces 100/20 = 5 bolts every second.

Together, Machine A and Machine B produces 3+5 = 8 bolts every second.

8 bolts / 1 sec = 200 bolts / x sec

Cross multiply, and get 200 = 8x; so, 25 = x.
So it takes 25 seconds to produce 200 bolts, when Machine A and Machine B work together.






Unfortunately, I'm having trouble following your logic. It looks like you try to find how much time it takes to produce 20 bolts, but then later try to figure out how many bolts are produced every 20 seconds?

I apply the simple formula: 1/(time taken by machine A) + 1/(time taken by machine B) = 1/(total time taken by both machines, together. this is now the rate (together). to get total time taken, inverse it. but i see what i did. i started adding the total bolts, thinking thats the time. i see my error, thank you. but the formula mentioned above (in my post) is correct, right?

Machine A .. 120 in 40 seconds then 3 /sec
machine B .. 100 in 20 seconds then 5/sec

in one sec both can produce 8.

so for 200 , 200/8 = 25

Time required = \(\frac{200}{\frac{120}{40} + \frac{100}{20}} = \frac{200}{8} = 25\)

Answer = B

Efficiency of machine A = 3 bolts/sec
Efficiency of machine B = 5 bolts/sec

Combined efficiency of the 8 bolts/sec

So, Time required to produce 200 bolts will be \(\frac{200}{8}\) = 25 seconds...

Answer will be (B) 25

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

Answer: B

machine A = 120/40 SECONDS = 3/sec
machine B = 100/20 seconds = 5/sec
A+B = 8/SEC
FOR 200 = 200/8 = 25SEC

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