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?

Answer:25 secondsStep-by-step explanation:Hi there! In order to answer this question, first we need to know how many bolts per second are produced by each machine, this can be known by dividing the number of bolts by the time it takes. For machine A:[tex]A = \frac{120 bolts}{40 s}= 3 \frac{bolts}{s}[/tex]For machine B:[tex]B = \frac{100 bolts}{20 s}= 5 \frac{bolts}{s}[/tex]So, if the two machines run simultaneously, we will have a rate of prodcution of bolts equal to the sum of both:[tex]A+B=(3+5)\frac{bolts}{s}=8\frac{bolts}{s}[/tex]Now, we need to know how much time it will take to producee 200 bolts, to find this out we need to divide the amount of bolts by the production rate:[tex]t = \frac{bolts}{ProductionRate}= \frac{200 bolts}{8 \frac{bolts}{s} }[/tex]The bolts unit cancell each other and we are left with seconds[tex]t = \frac{200}{8} s = 25 s[/tex]So it will take 25 seconds to produce 200 bolts with machine A and B running simultaneously.Greetings!