Algebra question involving motion.
- Thread starter TiaB
- Start date
Let t = number of hours traveled by the passenger train when it catches up with the freight
The freight train left 4 hours earlier than the passenger train, so it will have traveled four hours longer. So,
t + 4 = number of hours traveled by the freight train.
The two trains leave the same station, and travel in the same direction, so it should make sense that they will have traveled the SAME distance by the time the passenger train overtakes the freight train.
That is,
distance traveled by passenger train = distance traveled by freight train
A very important relationship between distance, rate(speed) and time is this:
distance = rate * time
The passenger train has traveled for t hours at a speed of 50 mph.
distance(for passenger train) = 50 mph * t hours, or 50t miles
The freight train has traveled for (t + 4) hours at a speed of 30 mph.
distance (for freight train) = 30 mph * (t + 4) hours, or 30(t + 4) miles
We've already said that the two distances must be equal in order for the passenger train to catch up with the freight. This gives us an equation:
50t = 30(t + 4)
Solve that for t. Then be sure to check to make sure that the two trains will, in fact, have traveled the same distance.
There are other ways to approach this problem, and perhaps one of the other volunteers will take a different approach. It happens that this one makes sense to me.
At 4 p.m. a freight train leaves chicago traveling 30 miles per hour. at 8 p.m. a passenger train leaves the same station traveling in the same direction at 50 mph. How long will it take the passenger train to overtake the freight train?
An alternate approach:
At 8 PM the freight train, moving at 30mph, has traveled 4(30) = 120 miles.
Once underway, the passenger train, moving at 50 mph, will close the gap between the two trains at the closing rate of 50 - 30 = 20 mph.
Being 120 miles apart to start, the passenger train will overtake the freight train in 120/20 = 6 hours.
An alternate approach:
At 8 PM the freight train, moving at 30mph, has traveled 4(30) = 120 miles.
Once underway, the passenger train, moving at 50 mph, will close the gap between the two trains at the closing rate of 50 - 30 = 20 mph.
Being 120 miles apart to start, the passenger train will overtake the freight train in 120/20 = 6 hours.