Q1- Distance, Time, and Speed An old car has to travel a 2-mile route, uphill and down. Because it is so old, the car can climb the first mile—the ascent—no faster than an average speed of 15 mi/h. How fast does the car have to travel the second mile—on the descent it can go faster, of course—to achieve an average speed of 30 mi/h for the trip?
There's the question. Doesn't state that the trip must take 4 minutes. The only place that was stated was in someone else's comment. And that person is wrong.
You must average 30mph the whole trip.
So... how does one determine average MPH for such a course?
If you drive 1 mile at 15 mph, and 1 mile at 45 mph, you will have gone 2 miles, and your average MPH is the two SPEEDS ADDED and then DIVIDED by the length (2). That gives 30 MPH average for a course length of 2 miles.
Doesn't matter how darn long it took. It isn't an issue in the question. There was no time limitation specified.
Doesn’t matter how darn long it took
If that’s true then it gets more complicated than the simple 15/45 answer. Once at the top of the hill how much time will it take to accelerate from 15mph to 45mph. That is an unknown factor and next to impossible to figure the mph necessary to offset this acceleration time to finally reach the 30mph average.
Einstein, himself, said there was no time left.
Doesn’t matter how darn long it took.
I think it does matter. To average 30mph the trip will take 4 minutes. You can go 100mph part of the trip and 10 mph some of it and 33mph some of it or 80mph some of it but the given is that you must average 30mph the whole trip. That is 4 minutes maximum allowed to make that 30mph average. You’ve used up 4 minutes going the first mile. No time left unless you can make it to the bottom of the hill instantaneously.