SOLUTION: Good day, can you help me in this trigonometry problem please? Each tire on a truck has a radius of 18 inches. The tires are rotating at 500 revolutions per minute. Find the

Algebra ->  Trigonometry-basics -> SOLUTION: Good day, can you help me in this trigonometry problem please? Each tire on a truck has a radius of 18 inches. The tires are rotating at 500 revolutions per minute. Find the      Log On


   

Question 980517: Good day, can you help me in this trigonometry problem please?

Each tire on a truck has a radius of 18 inches. The tires are rotating at 500 revolutions per minute. Find the speed of the truck to the nearest mile per hour.

Thank you.....
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!

Let us find the circumference  (the length of the circle)  of the radius  r = 18 inches.
It is   2%2Api%2Ar = 2*3.14*18 = 113.04 inches.

So,  when the wheel of the truck makes one rotation  (one revolution),  the truck moves  113.04  inches ahead.
When the wheel of the truck makes  500  rotations,  the truck moves  500*113.04 = 56520  inches ahead.  It is  56520%2F12 = 4710 feet.

So,  the speed of the truck is  4710 feet per minute.
It is  4710*60 = 282600 feet per hour,  or  282600%2F3 = 94200  yards per hour.  (Reminder:  1 yard = 3 feet).

Now,  to convert this speed to miles per hour,  we need to divide the value of  94200  by  1760,  because  1 mile = 1760 yards  (see the  article  from Wikipedia).

In this way you get the speed of  94200%2F1760 = 53.52 mi%2Fh.

Answer.  The speed of the truck is  54 mi%2Fh  (approximately).