1) Two cars leave town at the same time going in opposite directions. One travels 44 mi/h and the other travels 55 mi/h. In how many hours will they be 297 miles apart?

2) Two cars leave town at the same time going the same direction on the same road. One travels 32 mi/h and the other travels 47 mi/h. In how many hours will they be 69 miles apart?

1) The distance between them increases at a rate of 99 mph. Divide 297 miles by that number.

2) In this case, the distance between them increaes at a rate of 15 mph. Divide 69 miles by that number.

But what are the equations for me to solve them?

I need equations, that's what the directions are telling me.

separation speed = 44 + 55 = 99

99 t = 297

in time t, fast one goes 47 t

slow one goes 32 t
so
47 t - 32 t = 69

To solve these problems, we can use the concept of relative motion.

1) First, let's understand the situation. Two cars are moving in opposite directions. One car is traveling at 44 mi/h and the other at 55 mi/h. We need to find out how long it would take for them to be 297 miles apart.

To do this, we can consider their combined speed. Since they are moving in opposite directions, we can add their speeds together. The combined speed is 44 mi/h + 55 mi/h = 99 mi/h.

Now, we can use the formula distance = speed × time to find the time it takes for the two cars to be 297 miles apart. Rearranging the formula, we have time = distance / speed.

Plugging in the values, we get time = 297 mi / 99 mi/h = 3 hours.

Therefore, it will take 3 hours for the two cars to be 297 miles apart.

2) Here, two cars are moving in the same direction on the same road. One car is traveling at 32 mi/h and the other at 47 mi/h. We need to find out how long it would take for them to be 69 miles apart.

Again, we can consider their combined speed. Since they are moving in the same direction, we can subtract their speeds. The relative speed between the two cars is 47 mi/h - 32 mi/h = 15 mi/h.

Using the formula distance = speed × time, we can rearrange it as time = distance / speed.

Plugging in the values, we get time = 69 mi / 15 mi/h = 4.6 hours.

Therefore, it will take approximately 4.6 hours for the two cars to be 69 miles apart.