Answered

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



Answer :

AL2006
The space between them is shrinking at the rate of (4 + 5) = 9 mph.

The lake is 3 miles wide, so the space between them starts out at
3 miles, and shrinks to zero in 3/9 = 1/3 of an hour = 20 minutes.

Distance = Velocity * Time


Now, write the equations for the distance Jim and John each paddle as a function of time.


D_jim = 4 mph * time

D_john = 5 mph * time


And, the total combined distance that they both travel

D_total = D_jim + D_john

D_total = 4 mph * time + 5 mph * time

D_total = (4mph + 5mph) * time = 9 mph * time


Now, since they are both paddling from opposite sides of a river, when they meet, their total combined distance equals the width of the river, or 3 miles


3 miles = 9 mph * time

time = 3 miles / 9 mph = 1/3 hr = 20 minutes <== ANSWER

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