Question

The formula for finding the distance traveled, based on speed and time, is

D

=

R

T

D

=

R

T

, where


D is distance

R is rate (speed)

T is time


Units 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 160 minutes at an average speed of 17 miles per hour, how far was the ride, to 1 decimal place?

miles.


At what speed must a bicyclist ride to cover 12 miles in 1.5 hours, to 1 decimal place?

miles/hour.

Answer 1

Answer and explanation:

The formula for finding the distance traveled, based on speed and time, is $D=R\times T$

Where, D is distance , R is rate (speed)  and T is time

Units must be consistent.

1) Given : If the unit for D is miles and the unit for T is minutes.

To find : What must the units for R be?

Solution :

$R=\frac{D}{T}$

Now we put unit,

$R=\frac{miles}{minutes}$

The unit of R is miles per minute.

2) Given : If a bicyclist rides for 160 minutes at an average speed of 17 miles per hour.

To find : How far was the ride ?

Solution :

Speed R=17 miles per hour

Time T=160 minutes

Convert into hours,

$1\text{ minute}=\frac{1}{60}\text{ hour}$

$160\text{ minute}=\frac{160}{60}\text{ hour}$

$160\text{ minute}=2.67\text{ hour}$

Substitute value in the formula,

$D=R\times T$

$D=17\times 2.67$

$D=45.39\text{ miles}$

The distance is 45.4 miles.

3) Given : A bicyclist ride to cover 12 miles in 1.5 hours.

To find : At what speed must a bicyclist ride ?

Solution :

Distance D=12 miles

Time T=1.5 hour

Substitute value in the formula,

$R=\frac{D}{T}$

$R=\frac{12}{1.5}$

$R=8$

The speed is 8 miles per hour.