Distance

[Guest]

A train is to travel between two stations, A and C, on a timed schedule at 45 mph. It travels from A to an intermediate station, B, at 40 mph, then the speed increases to 50 mph. The train arrives on time at C. Compare distance of B and C from A.

Rate x Time = Distance, Distance / Rate = Time, Distance / Time = Rate formulas will not work, I don't think.

How do I proceed? Thanks.

[Guest]

If A to B is 40 miles then train takes 1 hour to go from A to B travelling at 40 mph
If B to C is 50 miles then train takes 1 hour to go from B to C travelling at 50 mph
That means it takes 2 hours to travel from A to C a distance of 90 miles
So average speed from A to C is (90 / 2) = 45 mph as stated in question.
Comparing the distances A to B and A to C is 40 miles and 90 miles respectively OR Ratio of 4 miles to 9 miles OR Ratio of 1 mile to 2.25 miles

[Guest]

Thanks again - simpler than I thought.