Suppose you purchased a brand new truck. The truck\'s speedometer was calibrated

Question

Suppose you purchased a brand new truck. The truck's speedometer was calibrated for stock tires having a diameter of 28 inches. After getting the truck you decided to replace the stock tires with new tires having a diameter of 30 inches. Unfortunately, you forgot to recalibrate your speedometer. As you were driving down the road, you noticed that a cop was behind you with his/her blue lights on. You looked down at your speedometer and it showed your speed at 60 mph in a 55 mph zone. Given that your truck was calibrated for the stock tires, you realized that you were actually not driving 60 mph. How fast, in mph. were you really driving?

Explanation / Answer

diameter of stock tires =28 inches =(28/12)ft

=>radius of stock tires r=(28/24)ft

v=60mph=60*5280 = 316800 ft/hr

v=rw

316800=(28/24)*w

=>w=316800*(24/28)

diameter of new tires =30 inches =(30/12)ft

=>radius  of new tires r=(30/24)ft

v=rw

v=(30/24)*316800*(24/28)

v=339428.57 ft/hr

v=339428.57/5280 miles/hr

v=64.286 miles/hr

really driving at 64.286 mph

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