My degree is in Mathematics, but I’ve never been good at word problems, like this one:
Suppose there are two trains on parallel tracks but heading in opposite directions.
The first train is headed East, and leaves the station at 6 PM going 40 miles per hour.
The second train is headed West, and leaves the station at 7 PM going 50 miles per hour.
If the stations are 400 miles apart, when will the trains meet?
One is “supposed” to come up with a cute formula, like
40(t+1)=400 – 50t
where t is travel time, in hours.
I have an easier time thinking of the problem this way:
The train heading East will be traveling an extra hour.
So, between the two trains, it’s necessary to cover 400-40, or 360 miles before the trains meet.
90 mph is the speed at which that 360 miles will be covered (40+50 mph). 360 divided by 90 is 4.
So, the trains will meet in 1+4 hours from 6 pm, or 11 pm.
If the train heading East is traveling at 30 mph, the trains will have to cover 370 miles from 7 pm on, and will meet in 1+370/80 hours, which makes figuring out time of day a messy business, indeed.