Question

Jim paddles from one shore of a lake 3 miles wide at 4 mph, and John paddles from the opposite shore a 5 pmh. How long will they travel before they meet

Answer 1

T = time that each will paddle before they meet

D = distance paddled by JIm

(3 - D) = distance paddled by John

D = 4T --- Equation 1

and

(3 - D) = 5T or

D = 3 - 5T --- Equation 2

Since Equation 1 = Equation 2

4T = 3 - 5T

9T = 3

T =1/3 hr = 20 minutes

ANSWER -- Jim and John will be paddling for 20 minutes before they pass each other

Answer 2

Let the time they both travel be x hours.

By the time they both meet, the distance covered by both would be equal to the width of the river.

Distance = Speed*time

The 4 mph after x hours would have traveled = 4x

The 5 mph after x hours would have traveled = 5x

Total distance traveled = 4x + 5x = 3

9x = 3

x = 3/9

x = 1/3 hours = 1/3 * 60 minutes = 20 minutes

They would have both traveled 20 minutes as at when they meet.