A blue train is 500m long and is travelling at 58km/h. A yellow train is 400m long and is travelling at 32km/h. The trains are travelling towards each other. Ooriginally, the trains are 900km apart.
A) how long will it take for the 2 trains to reach each other?
B) how many seconds after the front parts of the trains meet, will their rear parts pass each other?
A. 58 * t + 32 * t = 900 km.
90t = 900, t = 10 Hours.
B. V1 = 58km/h = 58,000m/3600s = 16.11 m/s.
V2 = 32km/h = 32,000/3600s = 8.89 m/s.
V1*t + V2*t = 900 m.
16.11t + 8.89t = 900, t = 36 s.
To find the time it takes for the two trains to meet, we need to consider their combined speeds as they are moving towards each other. Let's begin by converting the speed of the blue train from km/h to m/s.
A) How long will it take for the two trains to reach each other?
1. Blue train speed: 58 km/h
- Conversion to m/s: (58 km/h) * (1000 m/1 km) * (1 h/3600 s) = 16.1 m/s
2. Yellow train speed: 32 km/h
- Conversion to m/s: (32 km/h) * (1000 m/1 km) * (1 h/3600 s) = 8.9 m/s
Now that we have the speeds in m/s, we can find the time it takes for them to meet. We know that the trains have a combined distance of 900 km, and we want to find the time it takes for them to cover this distance.
3. Distance covered = Combined distance of the two trains = 900 km = 900000 m
4. Relative speed of the two trains = (16.1 m/s + 8.9 m/s) = 25 m/s
5. Time taken = Distance / Relative speed
- Time taken = 900000 m / 25 m/s = 36000 s
Therefore, the two trains will meet in 36000 seconds (or 10 hours).
B) How many seconds after the front parts of the trains meet will their rear parts pass each other?
To find this, we need to calculate the time it takes for the blue train to completely pass the yellow train.
1. Time taken by the blue train to pass the yellow train = Length of the yellow train / Relative speed
2. Length of the yellow train = 400 m
3. Relative speed of the two trains = 25 m/s (as calculated above)
4. Time taken = 400 m / 25 m/s = 16 s
Therefore, their rear parts will pass each other after 16 seconds.