A TRAIN B SPEEDING WITH 120KMPH CROSSES ANOTHER TRAIN C, RUNNING IN THE SAME DIRECTION IN 2 MINUTES. IF THE LENGTH OF THE TRAIN B AND C BE 100M AND 200M RESPECTIVELY. WHAT IS THE SPEED OF THE TRAIN C
Train B is faster than train C.
Train B's speed over train C has to travel 100m+200m in 2 minutes.
Excess speed = (100+200)/120 m/s
convert this to km/hr.
Add excess speed to 120 km/hr would then give the speed of train B.
To find the speed of Train C, we can use the concept of relative speeds.
When two objects are moving in the same direction, their relative speed is the difference between their individual speeds. In this case, the relative speed between Train B and Train C is the speed of Train B minus the speed of Train C.
Let's break down the given information to solve the problem:
- The length of Train B is 100m.
- The length of Train C is 200m.
- The time taken by Train B to cross Train C is 2 minutes.
To begin, we need to convert the time from minutes to hours to match the speed unit (km/h). There are 60 minutes in an hour, so 2 minutes is 2/60 = 1/30 hour.
To find the relative speed between the two trains, we use the formula:
Relative Speed = Distance / Time
The distance traveled by Train B to cross Train C is the sum of the lengths of the two trains: 100m + 200m = 300m.
Substituting the known values:
Relative Speed = 300m / (1/30)h
To convert the distance from meters to kilometers, we divide it by 1000 (1km = 1000m):
Relative Speed = (300m / 1000) km / (1/30)h
Simplifying further, we have:
Relative Speed = 9 km / (1/30)h
To find the speed of Train C, we need to subtract the speed of Train B from the relative speed.
Given that Train B is moving at a speed of 120 km/h, we have:
Speed of Train C = Relative Speed - Speed of Train B
= (9 km / (1/30)h) - 120 km/h
To find the speed of Train C, we need to simplify the equation further. First, we can convert 1/30 hour to minutes, because both trains have been defined in terms of speed in km/h and lengths in meters.
1/30 hour is equal to 2 minutes. So:
Speed of Train C = (9 km / 2 minutes) - 120 km/h
Now, let's convert 2 minutes to hours:
2 minutes is 2/60 = 1/30 hour.
Substituting the values, we get:
Speed of Train C = (9 km / (1/30)h) - 120 km/h
= (9 km / (1/30)h) - 120 km/h
= (9 km / (1/30)h) - (120 km/h * (30 minutes / 60 minutes))
= (9 km / (1/30)h) - (120 km/h * (1/2)h)
= (9 km / (1/30)h) - (60 km/h)
= (9 km / (1/30)h) - (60 km/h)
= 270 km/h - 60 km/h
= 210 km/h
Therefore, the speed of Train C is 210 km/h.