If Jim paddles from one shore of a lake 3 miles wide at 4 mph and John paddles from the opposite shore at 5 mph how long will they travel before they meet?

Answer 1

The answer is 20 minutes or 1/3 of an hour.

There is a very easy way to think about this type of problem. Instead of imagining two people paddling towards each other and meeting in the middle, imagine one person paddling all the way across the lake. Because they are traveling until they meet, no more and no less, together John and Jim will have covered exactly the entire distance of the lake. Because one is traveling at 4 mph and the other at five, they are covering distance at an combined speed of 9 mph. Now, the problem is simply finding out how long it takes to travel 3 miles at 9 mph. The equation looks like this:

(1 hour/ 9 miles) * 3 miles = (3/9) hours = (1/3) hours = 20 minutes

The standard equation for this type of word problem is speed x time = distance.

Here, the total distance is given (3 miles) and both Jim and John are paddling for the same length of time (T) until they meet.

4 mph x T (hours) = Jim's distance (miles)

5 mph x T (hours) = John's distance (miles)

4T + 5T = 3

9T = 3

T = 1/3 hour

and 1/3 hour times 60 minutes/hour = 20 minutes