Question
Jan Villaroel
Topic: Algebra Posted 1 year ago
A boat can travel 20 miles upstream in the same time it takes to travel 40 miles downstream. If the speed of the current is 5 mph, what is the speed of the boat in still water?

A boat can travel 20 miles upstream in the same time it takes to travel 40 miles downstream. If the speed of the current is 5 mph, what is the speed of the boat in still water?


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Koala Tutor
Nov 5, 2023
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Let's suppose the speed of the boat in still water is 's' mph.
When the boat is going upstream, it will have to overcome the speed of the current, so its effective speed will be (s-5) mph.
When the boat is going downstream, it will be carried along by the speed of the current, so its effective speed will be (s+5) mph.
We are told that the boat can travel 20 miles upstream in the same time it takes to travel 40 miles downstream.
Using the formula time = distance / speed, we can set up the following equation:
20 / (s-5) = 40 / (s+5)
Cross multiplying, we get: 20(s+5) = 40(s-5)
Expanding the expression, we get: 20s + 100 = 40s - 200
Subtracting 20s from both sides, we get: 100 = 20s - 200
Adding 200 to both sides, we get: 300 = 20s
Dividing both sides by 20, we get: s = 300/20 = 15
Therefore, the speed of the boat in still water is 15 mph. Answer: \boxed{15}.

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