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This is a question that is supplementary to my course work and is not required for marks. I find that it goes a bit beyond the scope of the material covered compared to the other questions. I understand the basics of rate and ratio but am struggling to equate the two ratios.

A machine has two gears that rotate at constant speeds. Every hour, Gear A completes exactly 2 more revolutions than Gear B. After some time, Gear A has completed 60 revolutions, and Gear B has completed 50 revolutions. How many revolutions does Gear A complete in one hour?

This is the source: https://courseware.cemc.uwaterloo.ca/42/assignments/1104/

The given answer is 12.

My friend gave me the following answer which I understand is correct, am wondering if this is the "traditional" way to solve it, or if anyone has any other insights. How would you have solved it?

b/b+2 = 50/60.

Also, could this be solved not as a ratio problem but as a linear equation?

Thanks!

Dan Murray
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1 Answers1

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Let Gear $A$ complete $a$ revolutions in an hour.
Let Gear $B$ complete $b$ revolutions in an hour.
Let the amount of hours elapsed be $t$.

Hence, we have

$$a = b + 2$$ $$at = 60, \, bt = 50$$ $$\therefore (b + 2)t = bt + 2t = 60, bt = 50$$ $$\therefore 50 + 2t = 60 \implies t = 5 \implies a = 12$$