A commuter travels to work at an average speed of u and returns home at an average speed v. Show that the average speed for the round trip is

2uv

_______

u+v

A commuter travels to work at an average speed of u and returns home at an average speed v. Show that the average speed for the round trip is

2uv

_______

u+v

Tutors, please sign in to answer this question.

Decatur, AL

Avg. speed = total distance/total time

distance = speed * t

Let d = distance to work or distance back home...

d = u * t

d = v * t

d/u = t

d/v = t

Total distance = 2*d = 2d

Total time = t

d/u + d/v = (dv + du)/uv

Avg speed for the whole trip = Total distance/total time

2d

--------

(dv+du)/uv

2d * (uv)/ (dv + du)

2duv/ (d(v+u))

The d's cancel:

(2uv)/(u+v)

Amaan M.

Math/Economics Teacher

New York, NY

5.0
(68 ratings)

Nafeesa M.

Expert SAT, ACT, Math, and French Tutor!

New York, NY

4.9
(115 ratings)

Wesley L.

Premier MIT Math Tutor and SHSAT/SAT/ACT Specialist

New York, NY

5.0
(228 ratings)

- Word Problem 4738
- Word Problem Help 1050
- Word Problems 1377
- Math Help 4872
- Algebra 1 3761
- Math Word Problem 3886
- Math Help For College 1306
- Algebra 4568
- Math 8627
- Algebra Help 939

## Comments