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?

1 Answer
Mar 26, 2017

Answer:

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.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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.