A freight train leaves the train station 44 hours before a passenger train. The two trains are traveling in the same direction on parallel tracks. If the rate of the passenger train is 11 mph faster than the freight​ train, how fast is each train traveling if the passenger train passes the freight train in 20 ​hours?
key concept: at catch-up time, they both will have travelled the same distance
rate of freight train ---- x mph
rate of passenger ----- x+11 mph
time taken by passenger = 20 hrs
time taken by freight = 64 hrs
distance covered by passenger tr. = 20(x+11)
distance covered by freight tr = 64x
64x = 20(x+11)
64x = 20x + 220
44x = 220
x = 5
Freight train averages 5 mph, the passenger train averages 16 mph ??????
check:
freight goes 64 hrs at 5 mph ----> 320 miles
pass. tr. goes 20 hrs at 16 hrs ---> 320 miles
My answer is correct, even though it is a rather silly question.
To solve this problem, we need to set up an equation based on the given information.
Let's denote the speed of the freight train as "x" mph. Since the passenger train is 11 mph faster than the freight train, its speed can be represented as "x+11" mph.
We know that the passenger train passes the freight train in 20 hours. Therefore, in 20 hours, the passenger train travels a distance equal to the distance the freight train travels in 20 hours plus the distance between the two trains at the beginning.
Now, let's define the distance as speed multiplied by time. The distance traveled by the passenger train in 20 hours is (x+11) * 20 mph, and the distance traveled by the freight train in 20 hours is x * 20 mph.
Since the freight train leaves the train station 44 hours before the passenger train, it has been traveling for 20 + 44 = 64 hours. In these 64 hours, the freight train has traveled a distance of x * 64 mph.
Since both trains are traveling in the same direction, the distance between them at the beginning is the distance traveled by the freight train in 64 hours minus the distance traveled by the passenger train in the same time. Therefore, we have the equation:
(x * 64) - (x * 20) = (x + 11) * 20
Now, we can solve this equation to find the speed of each train.
Expanding the equation:
64x - 20x = 20(x + 11)
Simplifying:
44x = 20x + 220
Subtracting 20x from both sides:
24x = 220
Dividing both sides by 24:
x = 220 / 24
Simplifying:
x = 9.17
Therefore, the speed of the freight train is approximately 9.17 mph, and the speed of the passenger train is 9.17 + 11 = 20.17 mph.