Question

A cyclist rides his bike at a rate of 33 feet per second. What is this rate in miles per hour? How many miles will the cyclist travel in 3 hours? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answers.

Answer 1

The cyclist will travel 1.125 miles in 3 hours.

Answer 2

The rate in miles per hour is 22.5 miles per hour.

67.5 miles will the cyclist travel in 3 hours.

Explanation:

Given : A cyclist rides his bike at a rate of 33 feet per second.

To find : What is this rate in miles per hour? How many miles will the cyclist travel in 3 hours?

Solution :

The fact given is 1 mile = 5280 feet.

A cyclist rides his bike at a rate of 33 feet per second.

Converting feet per second into miles per hour,

`1\text{ feet}=(1)/(5280)\text{ mile}`

`1\text{ second}=(1)/(3600)\text{ hour}`

`1\text{ feet/second}=(3600)/(5280)\text{ miles/hour}`

`33\text{ feet/second}=33* (3600)/(5280)\text{ miles/hour}`

`33\text{ feet/second}=22.5\text{ miles/hour}`

The rate in miles per hour is 22.5 miles per hour.

The time taken is 3 hours.

The distance covered is given by,

`\text{Distnace}=\text{Speed}* \text{Time}`

`\text{Distnace}=22.5* 3`

`\text{Distnace}=67.5`

Therefore, 67.5 miles will the cyclist travel in 3 hours.