2 TRAINS LEAVE 2 DIFFERENT CITIES THAT ARE 1735 MILES APART, IF TRAIN 1 GOES 45 MILES PER HOUR. IF TRAIN 2 GOES 25 MILES PER HOUR, HOW FAR FROM TRAIN 1'S STATION DO THEY PASS EACH OTHER?
The distance between them is shrinking at a rate which is equal to the sum of
their rates, or 45+25 or 70 mph.
We want to find out how long it will take for the 1735 mile distance between
them to shrink to zero, which is when they will pass each other.
We use time = distance/rate = 1735/70 = 347/14 hours.
In that length of time the train that goes 45mph will have traveled a distance
obtained from distance = rate*time = 45*(347/14) = 15615/14 = 1115 5/14 miles.
That's the answer.
To check it, we find the distance the other train has gone, also obtained from
distance = rate*time = 25*(347/14) = 8675/14 = 619 9/14 miles
If we add 1115 5/14 to 619 9/14 we get 1734 14/14 or 1735 miles. So it
checks.
Edwin