One train left the station and traveled toward its destination at a speed of 65 miles per hour. Later, another train left the station traveling in the opposite direction of the first train, it was going at a speed of 75 miles per hour. After the first train had traveled for 14 hours it was 1960 miles apart from the second train. How long did the second train travel?

Question

One train left the station and traveled toward its destination at a speed of 65 miles per hour. Later, another train left the station traveling in the opposite direction of the first train, it was going at a speed of 75 miles per hour. After the first train had traveled for 14 hours it was 1960 miles apart from the second train. How long did the second train travel?

Answer 1

add up the distances traveled:

65(14) + 75x = 1960

Hmmm. x=14, indicating they left at the same time. ??

Answer 2

To find out how long the second train traveled, we can use the formula:

Distance = Speed x Time

Let's break down the information given in the problem:

1. The first train traveled for 14 hours.
2. The first train's speed is 65 miles per hour.
3. The second train's speed is 75 miles per hour.
4. The distance between the two trains after 14 hours is 1960 miles.

Since the two trains are traveling in opposite directions, we can add the distances they traveled to get the total distance between them:

Distance of the first train = Speed of the first train x Time of the first train
Distance of the second train = Speed of the second train x Time of the second train

Total distance between the two trains = Distance of the first train + Distance of the second train

Let's calculate each distance separately:

Distance of the first train = 65 miles per hour x 14 hours = 910 miles
Distance of the second train = 75 miles per hour x Time of the second train

Total distance between the two trains = 910 miles + Distance of the second train

We know that the total distance between the trains after 14 hours is 1960 miles, so we can set up the equation:

1960 miles = 910 miles + Distance of the second train

To find the distance of the second train, we need to subtract 910 miles from both sides of the equation:

1960 miles - 910 miles = Distance of the second train

Now we can solve for the distance of the second train:

1050 miles = Distance of the second train

So, the distance traveled by the second train is 1050 miles.

Since we have the distance and the speed of the second train, we can use the formula above to find the time traveled by the second train:

Time of the second train = Distance of the second train / Speed of the second train

Time of the second train = 1050 miles / 75 miles per hour

Time of the second train = 14 hours

Therefore, the second train traveled for 14 hours.