Question

A turtle walks 7/8 of a mile in 50 minutes. What is the unit rate when the turtle’s speed is expressed in miles per hour?

a. To find the turtle’s unit rate, Meredith wrote the following complex fraction. Explain how the fraction 5/6 was obtained.
b. Determine the unit rate when the turtle’s speed is expressed in miles per hour.

Answer 1

a) when changing 50 minutes to hours get fraction
`(5)/(6)`

b)
`\text{Unit rate of turtle }=(21)/(20)` miles per hour

Explanation:

A turtle walks
`(7)/(8)` of a mile in 50 minutes.

Unit rate of turtle in miles per hours.

Unit rate means number of miles cover in 1 hours.

Distance =
`(7)/(8)` miles

Time = 50 minutes

1 minute =
`(1)/(60)` hour

50 minutes =
`(1)/(60)* 50` hours

`\text{Unit rate of turtle }=(7/8)/(5/6)`

`\text{Unit rate of turtle }=(21)/(20)` miles per hour

Part a)

`\text{Unit rate of turtle }=(21)/(20)` miles per hour

when changing 50 minutes to hours get fraction
`(5)/(6)`

Part b)

Unit rate of turtle is ratio of distance covered per unit of hours.

`\text{Unit rate of turtle }=(21)/(20)` miles per hour

Answer 2

21/20

Explanation:

a) One hour is equivalent to 60 minutes.

So we can multiply 50 minutes by the fraction
`(1 hour)/(60 minutes)`, so we could convert 50 minutes to hours.

It is:

`50 minutes * (1 hour)/(60 minutes)=(50)/(60)hours`

If we simplify the fraction, we have:

`50 minutes = (5)/(6)hours`

b) In order to express the turtle's speed in miles per hour, we have to divide

`(7)/(8)miles` by
`(5)/(6)hours`

So:

`((7)/(8)miles )/((5)/(6)hours )`

We simplify the expression by multiplying 7 mile by 6 and 8 by 5 hours:

`((7)/(8)miles )/((5)/(6)hours)=(42 miles)/(40 hours) =(21 miles)/(20 hours)`