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

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Katy, TX

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)

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