My teacher says everything is there to answer this question but i don't know. someone explain. two travellers spend from 12 o'clock to 6 o'clock walking along a level road, up a hill and back again. their pace is 4 mph on the level, 3 mph uphill, and 6 mph downhill. how far do they walk and at what time do they reach the top of the hill?

We can start with the basics. What we know is that this entire trip took 6 hours. So the travelers were able to walk on the level, uphill, and downhill in a total of 6 hours. 

A level mile takes 1/4 of an hour (15 minutes). An uphill mile takes 1/3 of an hour (20 minutes). A downhill mile takes 1/6 of an hour (10 minutes). So, to go and return over the same mile takes half an hour. This means that in 6 hours, they went 12 miles and came 12 miles back. So they went a total of 24 hours. 

If the 12 miles had been all level, it would have taken approximately 3 hours. It the 12 miles had been all uphill, it would have taken approximately 4 hours. When reaching the peak, 3.5 hours would have been the approximate time it took them to reach the top since it is in between. 

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.