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The speed of a stream is 5 mph. A boat travels 9 miles upstream in the same time it takes to travel 19 miles downstream. What is the speed of the boat in still water?

User Riko
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1 Answer

4 votes

Answer: 14 mph

Explanation:

Let x = the speed of the boat in still water.

Then the speed of the boat relative the bank of the river is u-5 km/hb when it moves upstream, and u+5 when it moves downstream.

We can write the basic equation for travel and distance problems

Time = Distance/Speed in the form

t = 9/x-5 for moving upstream, and

t = 19/x+5 for moving downstream.

Since the left side, t, is the same in both equations, you get a single equation for u

9/x-5 = 19/x+5

To solve it, multiply both sides by the product (x-5)*(x+5) and simplify:

9*(x+5) = 19*(x-5),

9x + 45 = 19x - 95,

45 + 95 = 19x - 9x,

10x = 140,

u = 140/10 = 14 mph.

hope this helps

User Enablor
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