# A paddleboat can travel 60 miles upstream in the same time it takes to travel 140 miles downstream. If the current of the river is 10 mph, what is the speed of the paddleboat in still water?

This is a a problem that will use the formula

Now that the time is equal, let's solve for t using the formula.

The boat's speed in meters per hour going upstream is equal to x - 10, and its speed going downstream is equal to x + 10.

In still water, the paddle boat can travel at a speed of 25 m/h.

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Let's denote the speed of the paddleboat in still water as (s) mph.

When the paddleboat travels upstream, it is moving against the current, so its effective speed is (s - 10) mph.

When the paddleboat travels downstream, it is moving with the current, so its effective speed is (s + 10) mph.

We can use the formula: [ \text{Time} = \frac{\text{Distance}}{\text{Speed}} ]

Given that the time taken for both upstream and downstream journeys is the same, we can set up the following equation:

[ \frac{60}{s - 10} = \frac{140}{s + 10} ]

Cross-multiplying, we get:

[ 60(s + 10) = 140(s - 10) ]

Expanding and simplifying:

[ 60s + 600 = 140s - 1400 ]

[ 600 + 1400 = 140s - 60s ]

[ 2000 = 80s ]

Now, divide both sides by 80 to solve for (s):

[ s = \frac{2000}{80} ]

[ s = 25 ]

So, the speed of the paddleboat in still water is (25) mph.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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