# Is this homework question missing information?

Here is the problem word for word:

Isaaic and Blaise decide to race. They both start at the same position at the same time. Isaaic runs at 2 m/s but decides to take a 2 minute rest stop. Blaise runs at half the speed and still wins by 10 meters. How far did Blaise run?

I can use only these equations.

X = VavgT

Vavg = (Vf - Vi)/T

A = (Vf - Vi)/T

Vf2 = Vi2 + 2ax

X = ViT + (1/2)at

This is as far as I've gotten.

Xb = (1m/s)Tb

Blaise's distance is equal to his average velocity times his time.

Blaise's time is equal to Isaaic's time + 120 seconds

Xb = (1m/s)(Ti + 120s)

Blaise's distance is equal to Isaaic's distance + 10 meters

Xi + 10m = (1m/s)(Ti + 120s)

but now i have no idea what to do. Shouldn't they have given me the acceleration? If we assume the acceleration to be 0 and try to solve for Ti, you end up dividing by 0 which leads nowhere.

Am I just not seeing the solution or is this problem missing some information?

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jhae2.718
Gold Member
We know that Blaise and Isaac run at constant speeds. Therefore, we can write their positions as a function of time. You've done this correctly for Blaise; you need to get an expression for Isaac's position.

Now, if you know that Blaise runs 10 m more than Isaac, how can you relate xb and xi, Blaise's and Isaac's final positions?

Set this as the final condition for Isaac's and Blaise's position functions (we'll call the time this happens at tf). You now have two equations with two unknowns and can solve it algebraically.

We know that Blaise and Isaac run at constant speeds. Therefore, we can write their positions as a function of time. You've done this correctly for Blaise; you need to get an expression for Isaac's position.

Now, if you know that Blaise runs 10 m more than Isaac, how can you relate xb and xi, Blaise's and Isaac's final positions?

Set this as the final condition for Isaac's and Blaise's position functions (we'll call the time this happens at tf). You now have two equations with two unknowns and can solve it algebraically.
ah! I remember now! Lol it's been so long since I've done this stuff, I'm actually trying to help my girlfriend with her physics homework. But I understand what you're saying and now I can explain it to her. The next step was so deceptively simple. Thanks :)

i'm not gonna lie i feel really stupid. i thought i understood this but i replied prematurely.

i'm still stuck.

i've got both isaac's and blaise's position as a function of time with these equations

Xi = (1m/s)(Ti + 120s) - 10m

Xb = (2m/s)(Tb - 120s) + 10m

and as for how to relate their final positions... Blaise wins by 10 meters so....

Xb = Xi + 10m

says that blaise's position is equal to isaac's position + 10 meters

Then what I thought I was supposed to do was input the expressions for Xi and Xb to solve

2m/s(Tb - 120s) + 10m = 1m/s(Ti + 120s) - 10m + 10m

So the above says Xb = Xi + 10m and then i thought I could solve from there.

But I still have two variables and it seems the only thing I can do is relate Tb in terms of Ti or vice versa. Am I on the right track or did I go wrong somewhere? If I'm going in the right direction, what do I do next?

jhae2.718
Gold Member
Your function for Isaac's position is wrong. Tb=Ti+120, so Isaac's position function should just have Ti, not +/- 120 s. You also switched Blaise's and Isaac's velocities.

I'd recommend letting the initial position of both be zero. If Isaac's position function is xi(t), then xi(tfinal)=xif, some final position. By the question, then, Blaise's final position xbf=xif+10.

This occurs at some time tfinal. We don't really care what it is for this question; we just need to rearrange one equation to equal tfinal, which we then substitute into the other and solve for xbf.

Your function for Isaac's position is wrong. Tb=Ti+120, so Isaac's position function should just have Ti, not +/- 120 s. You also switched Blaise's and Isaac's velocities.

I'd recommend letting the initial position of both be zero. If Isaac's position function is xi(t), then xi(tfinal)=xif, some final position. By the question, then, Blaise's final position xbf=xif+10.

This occurs at some time tfinal. We don't really care what it is for this question; we just need to rearrange one equation to equal tfinal, which we then substitute into the other and solve for xbf.
I finally came back to this problem a month and a half later after giving up. I spent about two hours dissecting your posts, reading them over and over to try to fully understand the help you were giving. I did manage to solve the problem and I realized a few things.

My equations were not wrong. You just did not take the time to fully read and understand them. Also, you made a mistake by saying Isaac's position function is Xi(t). I think what you meant to say was his position is determined by his velocity multiplied by his time, not that his position is determined by his position multiplied by time.

My problem was that I didn't understand the math required to isolate Ti on one side of the equation in order to solve for it. Unbelievably simple, I know, but I haven't done algebra in over 7 years.

I appreciate that you are willing to help, but please take the time to understand what people have written and to make sure that what you have written is correct. It's very frustrating to be pointed in the wrong direction and I'm a bit disheartened that no one else bothered to help.