How long will 2 trains 520 m long and 280 m long traveling at 38 km/hr and 30 km/hr respectively take to completely pass each when they are traveling in the same direction?
a) 6 min
b)12 min
c) 2 minutes
d) 1 minute
Thanks for your help!
Well the only way this works is if the 280 m train is completely in front of the 520 m train.
|---- 520 m ----| |-- 280 m --| ===>
Relative to the 280 m train, the 520 m train is going 8 km/h (why?).
Since we aren't given starting points, the problem must want us to start the clock when the front of the 520 m train is EVEN WITH the back of the 280 m train, and stop the clock when the back of the 520 m train is EVEN WITH the front of the 280 m train:
START:
|---- 520 m ----||-- 280 m --|
END:
|-- 280 m --||----520 m ----|
Of course they'll be on different tracks.
How far did the 520 m train travel? We can do this by measuring the distance traveled by a single point on it. Let's take the front of the train. It started even with the back of the 280 m train so by the time it was even with the front of the 280 m train it traveled.... 280 meters.
Now the entire 520 m train needs to be in front of the 280 m train. It does this 520 meters later when the back of the 520 m train is even with the front of the 280 m train (why?).
So it travels 280 m + 520 m = 800 meters to completely pass the 280 m train. This is 0.800 km. It does so at a rate of 8 km/hr relative to the 280 m train.
So finally we have t = d/r and so t = 0.800 km / 8km/hr = 0.100 hr = 6 minutes (A).
