Billy likes to go cycling

Question

His bike has wheels of diameter 85cm.

 

He has invented a counter for his bike,

which counts the number of revolutions

the wheels make.

 

One day the counter shows 150 revolutions.

 

How far has Billy cycled?

Give your answer to the nearest metre

 

 

 

 

 

Answer 1

Consider this example first: Suppose the circumference of your bike tire is a nice easy number like 3ft. 

 

If you're riding your tire and it rotates once, how far have you gone? 3ft

If it rotates twice, how far have you gone? 6ft

If it rotates four times, how far have you gone? 12ft

What if it rotates ten times? 

Or 57 times? 

 

How are you figuring this out?

 

You're multiplying the circumference by the number of revolutions. 

 

In this problem, you know your tires make 150 revolutions. To find out how far it has gone, you need to know their circumference. 

 

If you are given the diameter of the circle, the circumference is always going to be π times that diameter.

 

They tell you that the diameter of your tire is 85 cm. This means that the circumference of your tire must be 85π cm.

 

To find out how far you've traveled in cm, multiply this by the number of revolutions:

 

150 x 85π cm = 12750π cm

 

There are 100 cm in a meter, so divide this number by 100 to get the same distance in meters:

 

127.5π m

Answer 2

To change the units without changing the value, we use the Multiplicative Identity (that is, 1).

 

The formula for the circumference of a circle is:    C=Πd

The problem gives d=85 cm, so C=85Π cm.    So, (1 revolution)=(85Π cm) 

             or 1= (85Π cm) / (1 revolution)

 

Billy traveled:

     150 revolutions

     (150 revolutions)*1

     (150 revolutions) * ( (85Π cm) / (1 revolution) )      [note: revolutions cancel, leaving only cm]

     (150)*(85Π) cm

     40055.27 cm * ( (1 meter)/(100 cm) )

     401 meters        (rounded to nearest meter)