Finding a second velocity with a first and average velocity

[Heidi]

Homework Statement

A car travels along a straight line at a constant speed of 44.5 mi/h for a distance d and then another distance d in the same direction at another constant speed. The average velocity for the entire trip is 28.5 mi/h. NOTE: this is a practice problem.

Homework Equations

V_avg=(V_i+V_f)/2

The Attempt at a Solution

28.5=44.5/2+V_f/2
28.5*2-44.5=V_f
V_f=12.5 mi/h
This is not correct because the answer sheet says that the answer is 21 mi/h. I have been trying different ways including a proportionality using distance and time, but I cannot seem to get 21 as any of my answers. I feel as if none of the equations I have been given help with this problem because there is no acceleration or exact time and exact distance.

 

[MarkFL]

Try using a weighted average as your relevant equation, rather than the mean of the velocities, which assumes an equal time traveled at each velocity.

 

[Heidi]

Try using a weighted average as your relevant equation, rather than the mean of the velocities, which assumes an equal time traveled at each velocity.

How might I go about doing that then? It would give me two unknowns instead of just one.

 

[MarkFL]

How might I go about doing that then? It would give me two unknowns instead of just one.

I would begin by stating:

$\displaystyle\overline{v}=\frac{v_1t_1+v_2t_2}{t_1+t_2}$

Now, you are given $\overline{v}$ and using the relation $d=vt$, can you express the RHS in terms of everything else given, as well as the unknown velocity?

 

[kuruman]

Your expression for the average velocity (or more correctly speed in this case) is total distance traveled divided by total time required to travel that distance.

 

[Heidi]

I would begin by stating:

$\displaystyle\overline{v}=\frac{v_1t_1+v_2t_2}{t_1+t_2}$

Now, you are given $\overline{v}$ and using the relation $d=vt$, can you express the RHS in terms of everything else given, as well as the unknown velocity?

I would begin by stating:

$\displaystyle\overline{v}=\frac{v_1t_1+v_2t_2}{t_1+t_2}$

Now, you are given $\overline{v}$ and using the relation $d=vt$, can you express the RHS in terms of everything else given, as well as the unknown velocity?

I finally got it figured out. I was supposed to use the distance/speed formula. Thank you for your help anyway!