Average Velocity of a Car on a North-South Trip - Simple Velocity Question

[Mr Davis 97]

Homework Statement

A car makes a trip due north for three-fourths of the time and due south one-fourth of the time. The average northward velocity has a magnitude of 27 m/s, and the average southward velocity has a magnitude of 17 m/s. What is the average velocity (magnitude and direction) for the entire trip?

Homework Equations

$\displaystyle v_{avg} = \frac{x}{t}$

The Attempt at a Solution

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$\displaystyle v_{avg} = \frac{x}{t} = \frac{v_1t_1 + v_2t_2}{t} = \frac{v_1(\frac{3}{4}t) + v_2(\frac{1}{4}t)}{t} = \frac{3}{4}v_1 + \frac{1}{4}v_2 = \frac{3}{4}27 + \frac{1}{4}(-17) = +16~m/s$

Is this the correct answer for the average velocity over the whole trip? If not, what am I doing wrong?

 

[jbriggs444]

Is the southward velocity 7 or 17?

 

[Mr Davis 97]

Is the southward velocity 7 or 17?

Oops, it's 17 m/s. I fixed it.

 

[jbriggs444]

In that case, your work looks correct.

Edit: The question asks for magnitude and direction rather than a signed result.

 

[Mr Davis 97]

In that case, your work looks correct.

Edit: The question asks for magnitude and direction rather than a signed result.

Alright, I'll take that into account. Thanks!