A train left mooseport traveling west at 50 mph. One hour later, another train left mooseport traveling east at 70 mph. How many hours had the first train been traveling when they were 350 miles apart.
the trains are separating at 70+50=120 mi/hr
When the 2nd train left, they were already 50 miles apart.
So, the remaining 300 miles will take 300/120 hours.
Add that to the original hour head-start.
Let the time for the first train be t hrs
50t + 70(t-1) = 350
120t = 420
t = 420/120 = 7/2 or 3.5 hrs
To find out how many hours the first train had been traveling when they were 350 miles apart, we need to determine the time it took for the two trains to meet.
Let's consider the time it took for the second train to start traveling after the first train left. Since the second train left one hour later, it means that the first train had already been traveling for one hour when the second train started.
Now, we need to calculate the distance covered by both trains to meet each other. The first train, traveling at 50 mph for one hour, would have covered a distance of 50 miles. The second train, traveling at 70 mph for the time it took them to meet, covered a distance of x miles.
Since the total distance covered by both trains is 350 miles when they meet, we can write the equation:
50 + 70x = 350
To find x, we subtract 50 from both sides of the equation:
70x = 300
Finally, we divide both sides of the equation by 70 to solve for x:
x = 300/70 = 4.2857
So, the second train traveled for approximately 4.2857 hours when they were 350 miles apart.
Now, to answer the original question, we need to calculate how many hours the first train had been traveling when they were 350 miles apart. Since the first train traveled for one hour before the second train, we add this time to the time it took for the second train to cover the distance:
1 + 4.2857 = 5.2857
Therefore, the first train had been traveling for approximately 5.2857 hours when they were 350 miles apart.