Question

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 ?

What distance does the tourist have to cover?

Answer 1

The tourist has to walk `12` miles.

Explanation:

We can use the formula:

`"speed" = ("distance")/("time")`

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

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We know that the tourist must reach the station in some time `t` hours in order to catch the train. We also know that the station is some distance `d` miles away.

The tourist says that if his speed is `4 color(white)"-""mph"`, then he will be 30 minutes late (which is 0.5 hours). This means that he will travel `d` miles in `t + 0.5` hours.

`4 = d/(t+0.5)`

The tourist also says that if his speed is `5 color(white)"-""mph"`, then he will be 6 minutes early (which is 0.1 hours). This means that he will travel `d` miles in `t - 0.1` hours.

`5 = d/(t-0.1)`

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Now, we can take these two equations and use them to solve for `d`. But first, we will have to solve for `t` and then plug in `t` to find `d`.

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

`4 = d/(t+0.5) color(white)"XXXXX" 5 = d/(t-0.1)`

`4(t+0.5) = d color(white)"XXXX" 5(t-0.1) = d`

`4t+2 = d color(white)"XXXXXX" 5t-0.5 = d`

Now, we can set `4t+2` equal to `5t-0.5`, since we know that they are both equal to `d`.

`color(white)"X"4t + 2 = 5t - 0.5`
`4t + 2.5 = 5t`
`color(white)"XXX" 2.5 = t`

So the train leaves in `2.5` hours. Now that we know that, we can figure out what the distance was. Remember that the tourist said he would get to the station `30` minutes late if he walked at 4 mph. That means that he would get there in `3` hours instead of `2.5`. So, we can write:

`"speed" = "distance"/"time"`

`4 color(white)"-""mph" = d/(3 color(white)"-"""h")`

`12 color(white)"-""mi" = d`

So the train station is 12 miles away.