a train leaves a station and travels north at 85 km/hr. Four hours later, a second train leaves on a parrallel track and travels north at 125km/hr. How far from the station will they meet?
Train #1 = t hrs.
Train #2 = (t-4)hrs.
When train #2 catches up, they would have traveled the same distance:
d1 = d2.
85t = 125(t-4),
85t = 125t - 500,
125t - 85t = 500,
40t = 500,
t = 12.5 hrs.
d = Vt = 85 * 12.5 = 1062.5km.
To find out how far the two trains will meet from the station, we need to calculate the distance traveled by each train until they meet.
Let's start by finding the distance traveled by the first train. We know that the first train has been traveling for 4 hours at a speed of 85 km/hr.
Distance traveled by the first train = Speed × Time
Distance traveled by the first train = 85 km/hr × 4 hr = 340 km
Now, let's calculate the distance traveled by the second train. It started 4 hours later but has a faster speed of 125 km/hr. We can calculate this distance by considering the remaining time it takes for the second train to meet the first train.
Let the time taken by the second train to meet the first train be 't' hours. So, the second train has been traveling for 't' hours at a speed of 125 km/hr.
Distance traveled by the second train = Speed × Time
Distance traveled by the second train = 125 km/hr × t hr = 125t km
Since the two trains are traveling towards each other, the sum of their distances traveled until they meet will be the total distance from the station.
Total distance traveled = Distance traveled by the first train + Distance traveled by the second train
Solving for 't', we can set up an equation:
Distance traveled by the first train + Distance traveled by the second train = Total distance traveled
340 km + 125t km = Total distance traveled
Now, we need to find the total distance traveled. However, we don't have the specified time or distance when the two trains meet. Therefore, we can't calculate the exact distance from the station where they will meet.
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 assume that the distance from the station where they meet is denoted by d (in kilometers).
The first train travels at a speed of 85 km/hr for 4 hours, so it would have covered a distance of (85 km/hr) x (4 hr) = 340 km by the time the second train starts.
Now, let's find the time it takes for the second train to catch up to the first train.
Since the second train travels at a speed of 125 km/hr and needs to catch up the initial 340 km distance, the time it takes would be:
Time = Distance / Speed = 340 km / 125 km/hr = 2.72 hours
Now, we can find the distance from the station where they meet by multiplying the speed of the second train by the time it takes to catch up:
Distance = Speed x Time = 125 km/hr x 2.72 hr = 340 km
Therefore, they will meet 340 kilometers away from the station.