A train leaves a city heading west and travels at 50 miles per hour. Three hours later, a second train leaves from the same place and travels in the same direction at 65 miles per hour. How long will it take for the second train to overtake the 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.
don't get it
It will take 10h for the second train to catch up after it leaves. I think.
To find out how long it will take for the second train to overtake the first train, we need to calculate the time it takes for the second train to catch up to the first train.
Let's assume that the time it takes for the second train to catch up to the first train is T hours after the second train leaves.
In the time it takes for the second train to catch up, the first train has already been traveling for T + 3 hours (since it left three hours earlier).
Now we can use the equation: distance = speed × time to find the distance traveled by both trains.
The distance traveled by the first train is 50 miles per hour multiplied by (T + 3) hours, giving us a distance of 50(T + 3) miles.
The distance traveled by the second train is 65 miles per hour multiplied by T hours, giving us a distance of 65T miles.
Since the second train catches up to the first train when the distance traveled by both trains is equal, we can set up the following equation:
50(T + 3) = 65T
Now we can solve the equation to find the value of T:
50T + 150 = 65T
150 = 15T
T = 10
So, it will take the second train 10 hours to overtake the first train.