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word problems and turning them into algebraic equation to slove

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
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1 Answer

Avg. speed = total distance/total time
distance = speed * t

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

d = u * t1 , where t1 is the time taken
d = v * t2 , where t1 is the time taken

d/u = t1

d/v = t2

Total distance = 2*d = 2d

Total time = t1 + t2 = d/u + d/v

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

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


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

2duv/ (d(v+u))

The d's cancel:



You are most welcome Nancy.