# Average Speed

#### harpazo

What exactly is average speed? Can you provide an example?
Is the formula r = D/t?

#### Walagaster

MHF Helper
What exactly is average speed? Can you provide an example?
Is the formula r = D/t?
That formula can be used in this sense: If you traveled $D$ miles in time $t$ hours, you could say your average speed for the trip was $r = D/t$. That measure doesn't take into account any time taken for any stops or changes in speed along the way, but it does tell you that if you had traveled at exactly that average speed for the whole trip, you would get there in the same $t$ hours. If you have varying velocity it becomes a calculus problem.

2 people

#### harpazo

That formula can be used in this sense: If you traveled $D$ miles in time $t$ hours, you could say your average speed for the trip was $r = D/t$. That measure doesn't take into account any time taken for any stops or changes in speed along the way, but it does tell you that if you had traveled at exactly that average speed for the whole trip, you would get there in the same $t$ hours. If you have varying velocity it becomes a calculus problem.
Can you give me an actual average speed word problem at the algebra 2 level not calculus?

#### Zexuo

"If it took you two hours to walk a distance of six miles what was your average speed during the walk?"

2 people

#### Cervesa

A cyclist rides a distance of 10 miles from point A to B in half an hour. The return trip from B to A with the wind at her back takes 20 minutes.

What is her average speed for the round trip in miles per hour?

24 mph

3 people

#### DenisB

A cyclist rides a distance of 10 miles from point A to B in half an hour.
The return trip from B to A with the wind at her back takes 20 minutes.

What is her average speed for the round trip in miles per hour?
Harpazo, do you "see" that solution to above is simply: (10 + 10)/(1/2 + 1/3) ?

1 person

#### harpazo

"If it took you two hours to walk a distance of six miles what was your average speed during the walk?"
D = rt

Solve for r.

D/t = r

6/2 = r

3 = r

The average speed is 3 miles per hour.

#### harpazo

Harpazo, do you "see" that solution to above is simply: (10 + 10)/(1/2 + 1/3) ?
Yes, I do.

#### harpazo

A cyclist rides a distance of 10 miles from point A to B in half an hour. The return trip from B to A with the wind at her back takes 20 minutes.

What is her average speed for the round trip in miles per hour?

24 mph
Let A = average speed for round trip.

A = (10 + 10)/(1/2 + 1/3)

A = (20)/(5/6)

A = 20 • (6/5)

A = 4 • 6

A = 24 miles per hour

#### Debsta

MHF Helper
Let A = average speed for round trip.

A = (10 + 10)/(1/2 + 1/3)

Here 10 + 10 = 10miles +10 miles = 20 miles ; 1/2 +1/3 =1/2 hours + 1/3 hours = 5/6 hours. You don't need to write in the units, I'm just trying to point out that what you have done is good because the units match up (see other posts for when you do not do this)

A = (20)/(5/6) Units here are miles in numerator and hours in denominator = miles/hour or mph

A = 20 • (6/5)

A = 4 • 6

A = 24 miles per hour
Perfect. See my comment in red above about units.

1 person