Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 12 miles per hour slower than the westbound train. If the two trains are 400 miles apart after 2 hours, what is the rate of the eastbound train? No Rounding.
Well, it seems like these trains are going through a "differential" situation! Let's break it down:
Let the rate of the westbound train be x miles per hour. Since the eastbound train is traveling 12 miles per hour slower, its rate will be (x - 12) miles per hour.
Now, we know that distance = rate × time.
After 2 hours, the westbound train will have traveled a distance of 2x miles, while the eastbound train will have traveled a distance of 2(x - 12) miles.
Since they are 400 miles apart, we can write the equation:
2x + 2(x - 12) = 400
Now, let's solve for x:
2x + 2x - 24 = 400
4x - 24 = 400
4x = 424
x = 106
So, the rate of the westbound train is 106 miles per hour. Since the eastbound train is 12 miles per hour slower, its rate will be 106 - 12 = 94 miles per hour.
Therefore, the rate of the eastbound train is 94 miles per hour.
To find the rate of the eastbound train, we can set up a system of equations. Let's denote the rate of the eastbound train as "r" and the rate of the westbound train as "r + 12" (since the eastbound train travels 12 miles per hour slower than the westbound train).
We know that the two trains are 400 miles apart after 2 hours. Since they are traveling in opposite directions, we can add their distances together to get the total distance:
Distance traveled by the eastbound train: r * 2
Distance traveled by the westbound train: (r + 12) * 2
The sum of their distances should be equal to 400 miles:
r * 2 + (r + 12) * 2 = 400
Now we can solve this equation to find the rate of the eastbound train:
2r + 2(r + 12) = 400
2r + 2r + 24 = 400
4r + 24 = 400
4r = 376
r = 376/4
r = 94
Therefore, the rate of the eastbound train is 94 miles per hour.
Thanks you! I got the answer!
This is a classic Distance-Rate-Time problem
let the speed of slower train be x mph
then speed of faster train is x+12 mph
2x + 2(x+12) = 400
solve for x