Two trains leave stations 390 miles apart at the same time and travel toward each other. One train travels at 65 miles per hour while the other travels at 85 miles per hour. How long will it take for the two trains to meet?
let t hours be the time they meet
distance travelled by the slower train = 65t
distance travelled by the faster train = 85t
65t + 85t = 390
carry on
Well, these trains sound like they're in quite a hurry to meet each other! Let's do some math here.
The combined speed of both trains is 65 mph + 85 mph, which is 150 mph. So, they're zooming towards each other at a total of 150 miles per hour.
Since they started 390 miles apart, we can divide the distance by the speed to figure out how long it will take for them to meet.
390 miles divided by 150 mph gives us 2.6 hours. However, since we can't have fractional hours, we have to round up to the nearest whole number. So, it will take approximately 3 hours for the two trains to meet and say hello!
To find out how long it will take for the two trains to meet, we need to calculate the time it takes for them to cover a combined distance of 390 miles.
Let's suppose Train A is traveling at 65 miles per hour and Train B is traveling at 85 miles per hour. The total distance is 390 miles.
The equation we can use to solve for time is:
Distance = Speed * Time
For Train A: Distance = 65 * Time (in miles)
For Train B: Distance = 85 * Time (in miles)
Since they are traveling towards each other, the sum of the distances covered will be equal to the total distance of 390 miles:
65 * Time + 85 * Time = 390
Combining like terms:
150 * Time = 390
Now, let's solve for Time by dividing both sides of the equation by 150:
Time = 390 / 150
Time = 2.6 hours
Therefore, it will take approximately 2.6 hours for the two trains to meet.
To find out how long it will take for the two trains to meet, we can use the formula:
Time = Distance / Speed
First, we need to find out the combined speed of the two trains. As one train is traveling at 65 miles per hour and the other at 85 miles per hour, their combined speed would be:
Combined Speed = 65 mph + 85 mph = 150 mph
Now, we can use the formula to calculate the time:
Time = Distance / Speed
Time = 390 miles / 150 mph
To simplify the calculation, we can divide the numerator and denominator by 30:
Time = (390 miles /30) / (150 mph / 30)
Time = 13 hours / 5
Therefore, it will take 13 hours divided by 5, which is 2.6 hours, for the two trains to meet.