2steamers leave a port on a river at the same time, traveling in opposite directions. each is traveling 14 mph. how long will it take for them to be 56 miles apart.

Since they are traveling in opposite directions, their separation speed is the sum of their speeds: 14 mph + 14 mph = 28 mph. You can use the relationship

... time = distance/speed

to find the time until they are 56 miles apart.

... time = (56 mi)/(28 mi/h) = 2 h

It will take 2 hours for the steamers to be 56 miles apart.

You can make the problem more complicated by considering velocity (speed together with direction). If we say positive velocity is the speed downriver, one boat has a velocity of +14 mph, the other one, -14 mph. Then their speed of separation is the difference of these velocities: 14 mph - (-14 mph) = 28 mph. (To add another layer of complication, you can find the difference in the other direction (-14 -14 = -28), then find the magnitude (absolute value) of that, 28.)

If you want to add yet another layer of complication, you can add the speed of the river (s). Then one steamer is traveling at (-14 + s) and the other is traveling at (+14 + s). Their difference in speed is then (14+s) - (-14+s) = 28+s-s = 28.

I find it works nicely to consider the problem in the simplest possible terms. Whether the steamer speeds are considered to be relative to land or relative to water, their total is all that matters to this problem.

step-by-step explanation:

the answer is 128