How Do You Solve These Two Uniform Motion Problems?

[DB]

hey guys, in order to get the rest of problems on this sheet, i got to know how to do the first 2, and unfortunatly I am stuck, could u guys gimme a push in the right direction?

1. two cars are traveling in opposite directions at the speeds of 18 mph and 22 mph respectively. if they started from the same place and same time then in how many hours will they be 200 miles apart?

so far i got:
$$d_1+d_2=200$$

$$\Delta t=\frac{\Delta d}{v}$$
so

$$\Delta t=\frac{200-d_2}{v}$$

and

$$\Delta t=\frac{200-d_1}{v}$$

can i do this?:

$$\frac{200-d_2}{v}=\frac{200-d_1}{v}$$
if i can, then the algebra's got me stuck

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2. two cars started towards each other at the same time from points which are 300 km apart, and met in 5 hours. if one traveled twice the speed of the other, then wat were their speeds?

so far i know i have use:

$$v=\frac{\Delta d}{\Delta t}$$

and

$$v_1=x$$
$$v_2=2x$$

but then I am stumped, i know i need another equation with the 300 km but i can't see it :(

thanks in advance

 

[Doc Al]

The same approach will work for both problems.

For the first problem, realize that:
$$d_1 = v_1 t$$
$$d_2 = v_2 t$$

Just combine with your equation:
$$d_1+d_2=200$$
and solve for t.

For the second problem, just like the first problem you have:
$$d_1+d_2=300$$

And you have:
$$d_1 = v_1 t$$
$$d_2 = v_2 t = 2 v_1 t$$

This time t is known. Combine these and solve for $v_1$, and then $v_2$.

 

[DB]

wow i feel stupid its so easy! lol anyway i get 5 hours for the first n 20 km/h n 40 km/h for the second, thanks doc al.

 

[Doc Al]

anyway i get 5 hours for the first n 20 km/h n 40 km/h for the second

Right. Don't forget that in the second problem you need to find the speeds of both cars.