A train goes twice as fast downhill as it can go uphill,...

Question

A train goes twice as fast downhill as it can go uphill, and 2/3 feet as fast uphill as it can go on level ground. If it goes 120 miles per hour downhill, how long will it take to travel 45 miles per flat

Answer 1

ok, let's break this down. First, we identify three variables:

D = downhill speed U = uphill speed L = speed on level ground

They tell us D = 120 miles per hour.

Next, we know that D = 2 U. Using our algebra skills, that means that 120 = 2 U or 60 = U

Next, they say that it goes uphill at 2/3 of the level speed, so 2/3 L = U We know that U=60 so 2/3 L = 60. We can use the reciprocal shortcut here and multiply both sides by 3/2 (or multiply each side by 3 and then divide each side by 2 if you don't use the reciprocal shortcut, it is the same result). That means that L = (3/2)60 = 90 miles per hour

We need to go 45 miles on level ground. 45 is half of 90, so we are traveling for a half hour.