a train leaves a city heading west and travels at 50 miles per hour. three hours later, a second train laeves from the same place and travels in the same directionat 65 per hour. how long will it take for the second train to overtake first train?
To do these kind of questions, you have to ask yourself, what quantities are equal, so I can set up an equation.
When the second train overtakes the first, aren't the distances traveled by each equal ?
The slower train went t+3 hours, while the faster train only went t hours, right?
You know their rates, so can you find the distances they went?
let me know how you made out.
To find out how long it will take for the second train to overtake the first train, let's break down the problem step by step:
1. Start by determining the head start of the first train. Since it leaves 3 hours before the second train, the distance it travels during that time is given by:
Distance = Speed * Time
Distance = 50 miles/hour * 3 hours
Distance = 150 miles
2. Now that we know the head start distance is 150 miles, we need to calculate the relative speed between the two trains. To do this, subtract the speed of the first train from the speed of the second train:
Relative Speed = Speed of Second Train - Speed of First Train
Relative Speed = 65 miles/hour - 50 miles/hour
Relative Speed = 15 miles/hour
3. Since the second train needs to catch up with the first train, it can be viewed as closing a distance gap of 150 miles at a relative speed of 15 miles per hour. To calculate the time needed, divide the distance by the relative speed:
Time = Distance / Relative Speed
Time = 150 miles / 15 miles/hour
Time = 10 hours
Therefore, it will take the second train approximately 10 hours to overtake the first train.