Two trains heading toward each other are 400 miles apart. One train travels 15 miles per hour faster than the other train. If they arrive at the same station in 5 hours, how fast is each train traveling?
time = distance over speed
since the time is the same for both trains, and their combined distance is 400,
d/s = (400-d)/(s+15) = 5
d = 5s, so
(400-5s)/(s+15) = 5
s = 32.5
d = 162.5
check: 162.5/32.5 = 5
237.5/47.5 = 5
100
Let's assume the speed of the slower train is "x" miles per hour.
Since the faster train travels 15 miles per hour faster than the slower train, its speed can be represented as "x + 15" miles per hour.
Both trains are traveling towards each other, so the total distance covered by both trains is 400 miles.
The time taken by both trains to meet at the same station is 5 hours.
Using the formula: distance = speed * time, we can set up the equation:
Distance covered by slower train + Distance covered by faster train = Total distance
x * 5 + (x + 15) * 5 = 400
5x + 5(x + 15) = 400
5x + 5x + 75 = 400
10x + 75 = 400
10x = 325
x = 32.5
The speed of the slower train is 32.5 miles per hour.
The speed of the faster train is x + 15 = 32.5 + 15 = 47.5 miles per hour.
To get the answer, we can use the formula:
Distance = Speed × Time
Let's assume the speed of the slower train is x mph. Then, the speed of the faster train would be (x + 15) mph because it is stated that one train travels 15 mph faster than the other.
Now, let's calculate the distance each train travels:
Distance covered by the slower train = Speed of the slower train × Time = x mph × 5 hours
Distance covered by the faster train = Speed of the faster train × Time = (x + 15) mph × 5 hours
The total distance covered by both trains should add up to 400 miles since they are initially 400 miles apart:
Distance covered by the slower train + Distance covered by the faster train = 400 miles
(x mph × 5 hours) + ((x + 15) mph × 5 hours) = 400 miles
Now, we can solve this equation to find the value of x, which will give us the speed of the slower train.