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.

**Quote:**

why cant i do it this way:

take 1/time taken for each machine to produce 20 bolts: thats (1/60) for A plus (1/100) for B. Then I add them up and take the reciprocal to get total time taken. thats 37.45. so its 37.45 bolts every 20 secs. so that 106.8 seconds for 200 bolts.

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?

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