2 boats leave port heading in opposite directions. 1 at 12 mph and the other at 10 mph. how long before they are 33 miles apart

Question

2 boats leave port heading in opposite directions. 1 at 12 mph and the other at 10 mph. how long before they are 33 miles apart

Answer 1

First, I like to consider how the problem would work if one boat were standing still. If we just had one boat moving at 10 miles / hour, we would use the distance formula of Distance = Speed * Time. The distance we want is 33 miles, and the speed would be 10 mph, so:

 

33 miles = (10 miles / hour) * T hours

 

For a question like that, we would simply divide both sides by 10 mph, and we would get that 33 miles / 10 mph = 3.3 hours. Consider, however, if you were standing on the boat. It would feel like you are standing still, and the starting point where you were is moving away at 10 mph!

 

For this question, on the other hand, we have two boats moving in opposite directions! From the perspective of the starting point, it would look like the two boats started moving away from each other. However, imagine if you were standing on one of the moving boats. It would feel like you are standing still, and, relative to your position, the other boat would be moving away from you at your boat's speed of 10 mph plus the other boat's speed of 12 mph!

 

Since the two boats are moving in the exact opposite direction, their relative speed, or the speed they move relative to each other, is 10 mph + 12 mph, for a total of 22 mph. At that point, the equation is the same, Distance = Speed * Time.

 

33 miles = (10 mph + 12 mph) * T hours

33 miles = 22 mph * T hours

(33 miles) / (22 mph) = T hours

1.5 hours = T hours

 

So your final answer is 1.5 hours, or around 90 minutes!

Answer 2

Since the are moving in opposite directions, the rate at which the distance between them grows is equal to the sum of their speeds.

 

So the distance between them is increasing at the rate of 12 + 10 = 22 mph.

 

To find how long it will take for the distance between them to reach 33 miles, treat it just like any other rate problem:

 

rate x time = distance

22 mph x time = 33

time = 33 / 22 = 1.5

 

So the answer is 1.5 hours.