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.

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.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

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} ]

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7