Question

The formula for finding the distance traveled, base on the speed and time, is D= RT, whereD is distanceR is rateT is timeUnits must be consistent. If the unit for D is miles and the unit for T is minutes, what must the units for R be?_______Solve this formula for R.R=______If a bicyclist rides for 140 minutes at an average speed of 14 miles per hour, how far was the ride, to 1 decimal place?_______ miles.At what speed must a bicyclist ride to cover 60 miles in 1.5 hours, to 1 decimal place?______ miles/hour

Answer 1

Given:

a)

The formula for finding the distance traveled, based on the speed and time, is D= RT, where D is distance, R is rate and T is time.

The unit for D is miles and the unit for T is minutes.

b)

A bicyclist rides for 140 minutes at an average speed of 14 miles per hour.

c)

A bicyclist ride to cover 60 miles in 1.5 hours.

Required:

a)

We need to find the units fir R.

b)

We need to find the distance.

c)

We need to speed.

Step-by-step explanation:

a)

The given formula is

`D=RT`

Divide both sides of the equation by T.

`(D)/(T)=(RT)/(T)`
`(D)/(T)=R`

Substitute D =miles and T= minutes in the formula.

`miles=R* minutes`
`(miles)/(minutes)=R`

We can rewrite miles by the hour. since 60 minutes = one hour

`60\text{ }(miles)/(hour)=R`

The most common unit of speed is miles/ hour.

Answer:

The unit of R is miles/hour.

b)

T =140 minutes and R =14 miles per hour.

Convert the minutes onto hours.

Divide 140 by 60 to convert units.

`T=(140)/(60)hours`
`T=(7)/(3)hours`

Consider the formula.

`D=RT`

Substitute R =14 and T=7/3 in the formula.

`D=14*(7)/(3)`
`D=32.7miles`

Answer:

The bicycle was ridden 32.7 miles.

c)

D =60 and T =1.5

Consider the formula.

`D=RT`

Substitute D =60 and T =1.5 in the formula.

`60=R*1.5`

Divide both sides by 1.5.

`(60)/(1.5)=R*(1.5)/(1.5)`
`40=R`

Answer:

The speed of the bicycle is 40 miles/hour.

Final answer: