math problem?

Question

A train that travels a certain distance can go faster if the distance is farther, since it has more time to speed up and slow down. If this train travels 4 miles, it can go an average speed of 12 miles per hour. if it goes 8 miles, it can go an average speed of 14 miles per hour.

can you please show me how you set up the problem.

a. write the average speed as a linear function of the distance traveled.
b. what is the average speed of the train if it goes 10 miles?
c. write the time it takes to make a trip as a rational function of the distance
d. How far can the train go in one hour? what is its average speed?

I can't figure it out. please someone help me. I am stuck on this problem since yesterday. Promise I will not ask anymore questions just help me with this one.

Answer 1

Let v = average speed,
x = length of trip
then
a.
(v - 12) / (x - 4) = (14 - 12) / (8 - 4)
b. Substitute 10 for x
c. t = x/v
d. When t = 1 v is numerically equal to x

Answer 2

You've handed us the entire sequence of problems. I'll help at the start, since that's the basic sticking point for you.

You're given two data points: (4, 12) and (8, 14). Use these in your two-point formula to solve part (a). Use the function directly to solve part (b). Part (c) is done by inverting the function: solve it for distance, rather than speed (solve for y instead of x).
For the last one, you need to find the point that satisfies "if the train travels x miles, it can average x mph." Simply set x=y and solve.