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Can anyone help me solve these word problems.

  1. An automobile tire has a diameter of 30 inches how fast (r/m) does the wheel turn on the axle when the automobile maintains a speed of 45 mi/h?

  2. If an automobile wheel 78 cm in diameter rotates 600 r/min what is the speed of the car in km/h?

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  • $\begingroup$ I know the radius for the second one is 39 so would I use the formula for v=r(omega)? $\endgroup$ – Chino Grande Jun 25 '12 at 20:08
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The circumference of the wheel is $2.5\pi$ feet. At $45$ miles per hour, we are travelling at $\frac{(45)(5280)}{60}$ feet per minute.

So if $s$ is the number of revolutions per minute, we have $$(2.5\pi)s=\frac{(45)(5280)}{60},$$ and therefore $$s=\frac{(45)(5280)}{(60)(2.5\pi)}.$$ The rest can be done by calculator.

The other problem involves more or less the same ideas, but is a little easier. The circumference of the tire is $78\pi$ cm. At $600$ rpm, we travel $(78\pi)(600)$ cm per minute. This is $(78\pi)(600)(60)$ cm per hour. To convert to km per hour, divide by the number of cm in $1$ km, which is $100000$.

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  • $\begingroup$ I calculated, got $504.20286$. Maybe a glitch in handling the calculator? $\endgroup$ – André Nicolas Jun 25 '12 at 20:06
  • $\begingroup$ how would I set up the second problem.I see I made a calc error with the first one. $\endgroup$ – Chino Grande Jun 25 '12 at 20:07
  • $\begingroup$ I added to the answer. $\endgroup$ – André Nicolas Jun 25 '12 at 20:16
  • $\begingroup$ The final answer in my book is 88.2 $\endgroup$ – Chino Grande Jun 25 '12 at 20:18
  • $\begingroup$ I get $88.215922$. If you don't, you are not handling the calculator correctly. $\endgroup$ – André Nicolas Jun 25 '12 at 20:21

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