Simple physics problem

dexter

I'm trying to solve a problem for one of my mates who has to take a basic physics unit for his degree, but I can't sort out how to solve it. I feel completely lost without vectors or anything like that to work with.

It's actually a little bit embarrassing.. how would you go about solving this? x has a speed of 8km/s and y has a speed of 4.5km/s. x hits the finish line 78 seconds before y does. what's the distance from start to finish?

so all i could do was find that y is 351km behind when x hits the end. from there i over thought it and did some obscure things like dividing 351 by 0.56 and getting a distance of 626.78km. The way I solved this is hardly built off anything solid, so I doubt it's correct.

I know this is tragic, I have no idea why I can't do this. I could never be a teacher!

Thanks in advance, guys.

Fuzzy Cumulonimbus Cloud

Okay so Distance = Rate*Time
x (rate) = 8 km/s
y (rate) = 4.5 km/s
y (time) = x + 78
x (time) = y - 78
go from there

dexter

okay so I set up a simultaneous equation, and end up with 931.25km. how does this look? I'm terrible at these sorts of problems.

8(y-78)=4.5(x+78) etc.

Virum

Not quite. You have multiple unknowns and you have the difference in time twice as large as it should be.

You should have one variable for time, t.

x's time is just t,
y's time is t + 78

Note, both objects have to traverse the same amount of distance, just one takes longer. So we can say that:

d = 8t
d = 4.5(t+78)

If two things are equal to the same variable, they are equal to each other.

4.5(t+78) = 8t

Solve for t, and substitute into one of the equations to find distance.

dexter

Thanks a lot you two!