A freight train leaves Chicago traveling West at 35 mph. An hour later a passenger train leaves Chicago traveling on a parallel track at 60 mph. How far from Chicago will the passenger train catch up to the freight train?
let the distance traveled when the second catches up
be x miles
time for the freight train to go x miles = x/35
time for the faster train to go x miles = x/60
x/35 - x/60 = 1
times 420 , the LCD
12x - 7x = 420
5x = 420
x = 84 miles
check:
time for freight to go 84 miles = 84/35 = 2.4 hrs
time for faster train to go 84 miles = 84/60 = 1.4
which is a difference of 1 hour as required.
To find the distance at which the passenger train catches up to the freight train, we need to determine the time it takes for the passenger train to catch up.
Let's assume that the passenger train catches up to the freight train after t hours.
In the first hour, the freight train travels 35 miles because it is traveling at a speed of 35mph.
Since the passenger train starts an hour later, it will travel for t-1 hours when it catches up to the freight train.
During this time, the passenger train will cover a distance of 60(t-1) miles because it is traveling at a speed of 60mph.
The distance covered by the passenger train must equal the distance covered by the freight train when they meet, so:
35 + 60(t-1) = 35t
Now we can solve this equation for t:
35 + 60t - 60 = 35t
25 = 25t
t = 1
Therefore, the passenger train catches up to the freight train after 1 hour.
To find the distance from Chicago when this happens, we substitute t = 1 into the equation:
35 + 60(1-1) = 35(1)
35 + 0 = 35
So, the passenger train catches up to the freight train 35 miles from Chicago.