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if a ferris well take 45 seconds to make a complete rotation how many rotations will is complete in 3 hours

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2 Answers

Hi Jerry;
[(1 rotation)/(45 seconds)][(60 seconds)/(1 minute)][(60 minutes)/(1 hour)]=(x rotations)/(3 hours)
Let's note that the unit of seconds is in the numerator and denominator.  It cancels.
Let's note that the unit of minutes is in the denominator and numerator.  It cancels.
[(1 rotation)/(45 seconds)][(60 seconds)/(1 minute)][(60 minutes)/(1 hour)]=(x rotations)/(3 hours)
[(1 rotation)/(45)][(60)/(1)][(60)/(1 hour)]=(x rotations)/(3 hours)
The unit of rotations/hour is on both sides of the equation.  It cancels...
[(1 rotation)/(45)][(60)/(1)][(60)/(1 hour)]=(x rotations)/(3 hours)
[(1)/(45)][(60)/(1)][(60)/(1)]=(x)/(3)
(1/45)(60)(60)=x/3
80=x/3
Cross-multiply...
240=x
240 rotations will occur in 3 hours.
This is a great example of a unit conversion problem. The key is to have the final unit be the answer unit, in this case, rotations.
1 rotation/45 seconds * 60 seconds / minute * 60 minutes / hour * 3 hours = 3600*3/45 = 240 rotations.
 
Checking our work: 240 rotations * 45 seconds =10800 seconds or 180 minutes or 3 hours.