How Do You Calculate Average Speed with Variable Speeds and Distances?

[cstvlr]

Homework Statement

a) A journey is completed by travailing for the first half of the time at speed V1 and the second half at speed V2. Find the average speed Va for the journey in terms of V1 and V2 .

b) A journey is completed by traveling at speed V1 for half the distance and at speed V2 for the second half. Find the average speed Vb for the journey in terms of V1 and V2.

c) Deduce that a journey completed by traveling at two different speeds for equal distance will take longer than the same journey completed at the same two speeds for equal times.

Homework Equations

Va = d/t, where d = distance covered , t = time taken.

The Attempt at a Solution

a) d1 = distance covered by t1 and d2 distance covered by t2,
therefore 2d = V1t1+V2t2

I have no clue how to convert this in terms of V1 and V2

b) t1 = d/2v1 and t2 = d/2v2,

Va = d/t1 + d/t2

This is as far as I could go.

 

[jhae2.718]

On a), you've assumed that $d_1=d_2$. Since $d_1=\frac{v_1t}{2}$ and $d_2=\frac{v_2t}{2}$, take note of the fact that $d_1+d_2=d_{total}$ and $v_{avg}=\frac{d_{total}}{t_{total}}$, where $t_{total}=t$.

Try a similar approach on b), noting that $t_1+t_2=t_{total}$.

 

[cstvlr]

Thank you so much, I solved them.