A freight rain leaves a station and travels north at a constant rate of 60 mph. One hour later a passenger train leaves the same station traveling north on a parallel track at 80 mph. How long will it take for the passenger train to draw even with the freight train?
since distance = speed * time,
60(t+1) = 80t
Now just find t. That's the time traveled by the faster train.
Or, reason like this:
after 1 hour, the freight train is 60 miles ahead.
Since the passenger train goes 20 mi/hr faster, how long will it take to make up the 60 miles?
To find the time it takes for the passenger train to catch up with the freight train, we need to determine the distance between them.
Let's say T is the amount of time (in hours) it takes for the passenger train to catch up with the freight train. During this time, the freight train has been traveling for T+1 hours (since it left 1 hour earlier).
Now let's calculate how far each train has traveled during those times:
Distance traveled by the freight train = speed × time
Distance traveled by the passenger train = speed × time
The distance traveled by the freight train is 60 mph × (T + 1) hours, and the distance traveled by the passenger train is 80 mph × T hours.
Since the trains will be at the same distance when the passenger train catches up, we can set up an equation based on their distances:
60 mph × (T + 1) = 80 mph × T
Now we can solve this equation:
60T + 60 = 80T
Rearranging the equation:
60 = 80T - 60T
60 = 20T
Dividing both sides by 20:
T = 60 / 20
T = 3
Hence, it will take 3 hours for the passenger train to catch up with the freight train.