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?

  • $\begingroup$ 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

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 $100000$.

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.