# A tourist calculated that if he walks to the railroad station with a speed of 4 mph, he’ll miss the train by half an hour, but if he walks with a speed of 5 mph, he’ll reach the station 6 minutes before the departure of the train ?

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What distance does the tourist have to cover?

What distance does the tourist have to cover?

The tourist has to walk

We can use the formula:

To create two equations we can use to solve this problem.

We can multiply both equations by the denominator to get that:

So the train station is 12 miles away.

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Let ( t ) be the time it takes for the tourist to reach the station. The distance to the station is the same in both scenarios. Using the formula ( \text{distance} = \text{speed} \times \text{time} ), we can set up the equations:

For walking at 4 mph: [ 4(t + 0.5) = \text{distance} ]

For walking at 5 mph: [ 5(t - \frac{6}{60}) = \text{distance} ]

Equating the distances: [ 4(t + 0.5) = 5(t - \frac{6}{60}) ]

Solve for ( t ): [ 4t + 2 = 5t - 0.1 ] [ 2 = t - 0.1 ] [ t = 2.1 \text{ hours} ]

The distance to the station is: [ \text{distance} = 4 \times (2.1 + 0.5) = 10.6 \text{ miles} ]

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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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