# Simple problem I thought

I assigned a couple of problem to my students today without realizing that these would be too difficult for high school students. However, after starting the problem, I got stumped. I know I am missing something, but what is it? The problem reads as follows:

5. A person walks first at a constant speed of 5.00 m/s along a straight line from point A to point B and then back along the line from B to A at a constant speed of 3.00 m/s. What is
a. her average speed over the entire trip and
b. her average velocity over the entire trip?

Part b is simple, but 'a' is where I got stuck. You know delta x is the same, and you know that t1 and t2 will be different as well.

So, delta x = v1*t1, and x=v2*t2.

However this leaves us with three unknowns and two equations.

What am I missing for my third equation?

Thanks!

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x= distance traveled from A to B
v_1=5 m/s
v_2=3 m/s

x=5t_1
x=3t_2

t_1=x/5
t_2=x/3

avg. speed = distance/total time= 2x/(t_1 +t_2)=(2x)/(x/3+x/5)=3.75 m/s

one of your unknowns simply cancels out.

since the average speed will be the same no matter what the distance, it is unimportant what the distance between a and b are.

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Thanks,

I knew it was something like that.

HallsofIvy