A train leaves the station and travels north at a speed of 75 mph. Two hours later, a second train leaves on a parallel track and travels north at 125 mph. How far from the station will they meet?
75*2 + 75t = 125t,
t = 3h.
d = 125 * 3 = 375 Miles.
Key concept:
they will have travelled the same distance
time taken by the slower train ---- t hours
time taken by the faster train ----- t-2 hrs
125(t-2) = 75t
solve for t , sub into either 75t or 125(t-2)
To find the distance from the station where the two trains meet, we need to determine the time it takes for the second train to catch up to the first train.
Let's first find the head start distance of the first train. Since it travels for 2 hours before the second train starts, we can calculate its head start distance by multiplying its speed by the 2-hour time gap:
Head start distance = 75 mph * 2 hours = 150 miles
Now, let's find the relative speed of the second train compared to the first train:
Relative speed = Speed of the second train - Speed of the first train
= 125 mph - 75 mph
= 50 mph
Since the second train is catching up to the first train, we can think of their meeting point as the point where the second train covers the head start distance of the first train at their relative speed.
Time taken for the second train to catch up = Head start distance / Relative speed
= 150 miles / 50 mph
= 3 hours
Therefore, the two trains will meet 3 hours after the second train leaves the station.
Now, to find the distance from the station where they meet, we can use the formula:
Distance = Speed of the second train * Time taken for the second train to catch up
= 125 mph * 3 hours
= 375 miles
Therefore, they will meet 375 miles from the station.
To find the distance from the station where the two trains will meet, we need to determine the time it takes for the second train to catch up to the first train.
Let's denote the distance from the station where they meet as "d" and the time it takes for the second train to catch up as "t".
Since the first train leaves two hours earlier, it has a head start of 75 mph x 2 hours = 150 miles.
Now, let's consider the relative speed between the two trains. The relative speed is the difference between their speeds.
Relative speed = 125 mph - 75 mph = 50 mph.
We can use the formula: Distance = Speed x Time to find the time it takes for the second train to catch up, where the distance is the head start distance + the distance the second train travels.
So, d = (75 mph x t) + (150 miles + 125 mph x t).
Simplifying the equation, we get:
d = 75t + 150 + 125t.
Now, we can solve for "t". Combine the "t" terms and move the constant term to the right side of the equation:
d = 200t + 150.
Next, isolate "t" by subtracting 150 from both sides:
d - 150 = 200t.
Finally, divide both sides of the equation by 200:
t = (d - 150) / 200.
Therefore, the two trains will meet at a distance "d" from the station after a time "t" given by t = (d - 150) / 200.
To find the exact distance, we need more information, such as the time it takes for the second train to catch up or the distance traveled by the second train until they meet.