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The radius of the wheel on a bike is 27 inches. If the wheel is revolving...

The radius of the wheel on a bike is 27 inches. If the wheel is revolving at 144 revolutions per minute, what is the linear speed of the bike, in miles per hour? Round your answer to the nearest tenth, and do not include units in your answer.

Expert Solution

Given -----> radius of the wheel on a bike is 27 inches

the wheel is revolving at 144 revolutions per minute

We know that in 1 revolution, wheel will cover a distance equal to its circumference.

Circumference = 2*π*r where r ---> radius of the circle

Circumference of the wheel ---> 2*π*27 = 169.64 inches

So in 1 minute the wheel travels 169.64 inches

wheel travels 169.64 inches in 1 minute

1 mile = 63360 inches

1 / 63360 miles = 1 inch

169.64 / 63360 miles = 169.64 inches

So , in 1 revolution the wheel travels 169.64 inches

in 144 revolutions the wheel travels 169.64*144 inches = 24428.16

Now 60 minutes = 1 hour

1 minute = 1 / 60 hours

So wheet is trvelling at a speed of 169.64 inches / 1 minute

So wheet is trvelling at a speed of ( 169.64 / 63360 ) miles / ( 1 / 60 ) hours

=> ( 169.64 / 63360 )*60

=> 0.0026*60 = 0.16 miles / hour

Now for 144 revolution

( 169.64 / 63360 )*60*144

==> 23.13 miles / hour ~ 23.1 miles

milcah answered 2 years ago

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