1. ## [SOLVED] Speedometer

The speedometer of a small pickup truck is designed to be accurate with tires of radius 14 inches.
a. find the number of rotations of a tire in 1 hour if the truck is driven at 55 mph.
b. suppose that oversize tires of radius 16 inches are placed on the truck. if the truck is now driven for 1 hour with the speedometer reading 55 mph, how far has the truck gone? if the speed limit is 55 mph, does the driver deserve a speeding ticket?

2. Hello somanyquestions
Originally Posted by somanyquestions
The speedometer of a small pickup truck is designed to be accurate with tires of radius 14 inches.
a. find the number of rotations of a tire in 1 hour if the truck is driven at 55 mph.
b. suppose that oversize tires of radius 16 inches are placed on the truck. if the truck is now driven for 1 hour with the speedometer reading 55 mph, how far has the truck gone? if the speed limit is 55 mph, does the driver deserve a speeding ticket?
Here's how to work (a) out:

• Work out the circumference of the tyre in inches.
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• Work out how many inches the truck moves forward in 1 hour.
.
• Divide the second answer by the first; that will tell you how many rotations the tyre needs to make.
To work out (b), it's easiest to use ratios and multiplying factors. If you don't know how to use them, I did a question involving them recently just here.

The ratio of the radii of the two sets of tyres is $14:16 = 7:8$. With bigger tyres, the truck will move forward a greater distance for a given number of rotations of the wheels. To find the new distance you will therefore multiply the first one ( $55$ miles) by $\frac87$. This tells you how far the truck goes in an hour, and therefore its speed in mph.

So, yes, I think he probably does deserve a ticket.

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