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

Accepted Solution

Answer:   Cassie is traveling 63.6 mphStep-by-step explanation:If the three numbers, left to right, are A, B, C, then the tire radius in millimeters is ...   A×B/100 + 12.7×CFor the factory tires, the tire radius is ...   240·75/100 + 12.7·16 = 180 +203.2 = 383.2 . . . . millimetersFor the replacement tires, the tire radius is ...   290·70/100 +203.2 = 406.2 . . . . millimetersThe 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_____Comment on the problem statementCaroline'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.