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

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.

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

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