word problems and turning them into algebraic equation to slove

Question

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

Answer 1

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
--------
(dv+du)/uv


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

2duv/ (d(v+u))

The d's cancel:

(2uv)/(u+v)