A train leaves a station and travels north at a speed of 105 mph. Two hours later, a second train leaves on a parallel track and travels north at 135 mph. How far from the station will they meet?

Question

A train leaves a station and travels north at a speed of 105 mph. Two hours later, a second train leaves on a parallel track and travels north at 135 mph. How far from the station will they meet?

please help

Answer 1

Since distance = speed * time,

210+105(t-2) = 135(t-2)
t=9, so the distance = 7*135 = 945 mi

or, since the time is the same once both trains are moving, if the distance each has traveled is d,

(d-210)/105 = d/135
d = 945

Answer 2

To find the distance from the station where the two trains will meet, we can use the formula:

Distance = Speed × Time

Let's break down the information given:

First Train:
- Speed = 105 mph
- Time = t + 2 hours (since it leaves 2 hours earlier than the second train)

Second Train:
- Speed = 135 mph
- Time = t (since it starts at the same time as the first train)

Now, we need to set up an equation to represent the distance traveled by each train:

Distance of First Train = Distance of Second Train

Using the formula Distance = Speed × Time, we have:

105(t + 2) = 135t

Now, let's solve this equation to find the value of t, and then calculate the distance where they will meet:

105t + 210 = 135t (Distributing 105 to t and 2)
210 = 30t (Subtracting 105t from both sides)
t = 210/30 (Divide by 30 to isolate t)
t = 7 hours

Now that we know the value of t, we can substitute it into either equation to find the distance. Let's use the second train's equation:

Distance of Second Train = Speed × Time
Distance = 135 × 7
Distance = 945 miles

Therefore, the two trains will meet approximately 945 miles from the station.

Answer 3

To solve this problem, we can use the concept of relative motion. We need to find the distance from the station where the two trains will meet.

Let's assume that the two trains meet after time 't' hours.
The first train leaves 2 hours earlier, so it would have traveled for a total of (t + 2) hours.
The second train, which left 2 hours later, would have traveled for a total of 't' hours.

Since distance = speed × time, we can say that:
Distance covered by the first train = 105 × (t + 2)
Distance covered by the second train = 135 × t

Since both trains meet at the same point, the distances traveled by both trains should be equal.
Therefore, we can set up an equation:

105 × (t + 2) = 135 × t

Now, let's solve for 't':

105t + 210 = 135t (distributing 105 to t and 2)
210 = 135t - 105t (combining like terms)
210 = 30t
t = 210/30
t = 7

Therefore, the trains will meet after 7 hours.

To find the distance from the station where they will meet, we can substitute the value of 't' back into any of the earlier equations. Let's use the equation for the distance covered by the second train:

Distance covered by the second train = 135 × t
Distance = 135 × 7
Distance = 945 miles

So, the two trains will meet approximately 945 miles from the station.

A train leaves a station and travels north at a speed of 105 mph. Two hours​ later, a second train leaves on a parallel track and travels north at 135 mph. How far from the station will they​ meet?

Since distance = speed * time,

To find the distance from the station where the two trains will meet, we can use the formula:

To solve this problem, we can use the concept of relative motion. We need to find the distance from the station where the two trains will meet.

A train leaves a station and travels north at a speed of 105 mph. Two hours later, a second train leaves on a parallel track and travels north at 135 mph. How far from the station will they meet?