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Caroline replaced the original factory tires (P240/75 R 16) on her pickup truck with P290/70R16 tires. If the speedometer on Cassie’s truck reads 60 mph, how fast is Cassie actually traveling?

Cassie is traveling 65.7 mph
Cassie is traveling 66.6 mph
Cassie is traveling 68.9 mph
Cassie is traveling 63.6 mph

User Proseosoc
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1 Answer

1 vote

Answer:

Cassie is traveling 63.6 mph

Explanation:

If the three numbers, left to right, are A, B, C, then the tire radius in millimeters is ...

A×B/100 + 12.7×C

For the factory tires, the tire radius is ...

240·75/100 + 12.7·16 = 180 +203.2 = 383.2 . . . . millimeters

For the replacement tires, the tire radius is ...

290·70/100 +203.2 = 406.2 . . . . millimeters

The speedometer is calibrated based on the number of revolutions the tire makes in a given time period. If the truck goes farther for each revolution, its speed is higher by the same proportion.

If the speedometer on the truck with these replacement tires reads 60 mph, the actual speed is ...

(406.2/383.2)×60 mph = 63.6 mph

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Comment on the problem statement

Caroline's truck has the replacement tires. If Cassie's speedometer reads 60 mph, we have no reason to assume Cassie is traveling at any speed other than 60 mph.

User Mlevit
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