Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 10 miles per hour slower than the eastbound train. If the two trains are 720 miles apart after 4 hours, what is the rate of the westbound train?
well, their combined rate is 720/4 = 180 mi/hr
Question 20
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at
65
miles per hour. The westbound train travels at
75
miles per hour. How long will it take for the two trains to be
252
miles apart?
To find the rate of the westbound train, we can set up an equation based on the given information.
Let's suppose the rate of the eastbound train is 'x' miles per hour. Since the westbound train is traveling 10 miles per hour slower, its rate would be 'x - 10' miles per hour.
Now, we know that the two trains are 720 miles apart after 4 hours. This means that the total distance traveled by both trains is 720 miles.
The distance traveled by the eastbound train is equal to its rate multiplied by the time it traveled, which is 4 hours. So we have:
Distance traveled by the eastbound train = x * 4
Similarly, the distance traveled by the westbound train is equal to its rate (x - 10) multiplied by the time it traveled, which is also 4 hours. So we have:
Distance traveled by the westbound train = (x - 10) * 4
Now, adding both distances together gives us the total distance between the two trains:
x * 4 + (x - 10) * 4 = 720
We can simplify this equation:
4x + 4(x - 10) = 720
Now, solve for x to find the rate of the eastbound train:
4x + 4x - 40 = 720
8x - 40 = 720
8x = 760
x = 95
Therefore, the rate of the westbound train (x-10) is 95 - 10 = 85 miles per hour.