Car and SUV meeting on a North-South highway

[Tyrannosaurus_]

Homework Statement

On a North-South highway, a Car drives 80 km/h [N]. A SUV, that is north of the Car, is moving 70 km/h [South]. The car is to the south of the SUV. The two are separated by 20 km. Where are the two cars when they pass each other.

Homework Equations

Both are in uniform motion so V = d/t -> d = v*t

The Attempt at a Solution

d_c + d_suv = 20 km <--- this is my question... this part okay?
v_c*t + v_suv*t = 20 km
t*(v_c + v_suv) = 20 km
t*(160 km/h) = 20 km
t = 20 km / 160 km/h
t = 1/8 h

Next
d_c = v_c*t
d_c = 90 km/h* (1/8) h
d_c = 90/8 km [N]

So, the two meet at a place 90/8 km to the north of where the car started the problem from

 

[scottdave]

You originally stated that the car's speed was 80 km/h. Was that a mistake? Is it really supposed to be 90?

 

[Tyrannosaurus_]

Sorry, that's a typo when I subbed the speed for the car. It should be as stated, the 80 km/h.

Do you think it's okay that I set the sum of their displacements to 20 km?
Also, should I subtract their velocities (they're act in opposite directions) when common factoring the time, t?

 

[scottdave]

You add, not subtract. Think like this: each car is covering a distance. Both distances contribute to make the 20 km total. You could instead write it as 2 equations, with one car covering distance x, and the other car distance is (20 - x)

 

[ZapperZ]

Why is it OK to do this problem without a sketch?

Zz.

 

[Tyrannosaurus_]

Hi ZapperZ,

I've drawn sketches on my notes, but can't draw in this box. Moreover, I've posted images of my solutions before and have been in "trouble" for not following the template.

Thanks for your "help" though ZapperZ - lol!