# 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?

##### 1 Answer

The tourist has to walk

#### 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

The tourist says that if his speed is

#4 = d/(t+0.5)#

The tourist also says that if his speed is

#5 = d/(t-0.1)#

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Now, we can take these two equations and use them to solve for

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

#color(white)"X"4t + 2 = 5t - 0.5#

#4t + 2.5 = 5t#

#color(white)"XXX" 2.5 = t#

So the train leaves in

#"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.