# Math Help - degree problem

1. ## degree problem

Am I suupose to convert 207 miles to radians? Sorry I'm so lost...
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The diameter of the wheels on your car (including the tires) is 25 inches. You are going to drive 207 miles today. Each of your wheels is going to turn by an angle of __________ degrees.

and

You travel again in your trusty car with the 25 inch wheels. You installed a nifty gadget that measures how often your wheels turn each hour. It shows that right now they turn 55000 times per hour. You figure you are going at a speed ________ of miles per hour.

2. I may be wrong, since I'm not used calculating in miles and inches. As far as I know 1 mile should have 63360 inches (google said so...)

Since the diameter is 25, then the radius is 12.5. Then circumference of the tire is: $2\pi\cdot 12.5 = 25\pi \; \text{inches}$
Now 207 miles are : 1.311552 *10^7 inches.
If you divide the whole distance with the circumference, you get the number of turns your car did. (1.67* 10^5)
Multiplicate this by 360 and you get your wished degrees. (6.01 *10^7)

For the second question, ask your teacher whether you are supposed to have constant speed during that hour or not. Since it necessary to know. If the speed is not constant, you can't find out. So we suppose it is constant:
55000 times make a distance of : $55000 * 25\pi = 4.32 *10^6 \;inches$
Divided by 63360 you get 68.2 miles in one hour. That's your speed 68.2 mph