How long will two trains 520 meter and 280 meter long and traveling 38 km per hour and 30 km per hour respectively, take to pass one another completely when they are traveling in the same direction?
Text book explanation is
[(520+280)x0.001]/8
but I need a logical explanation and better way to solve this.
Thank you
So the 520 meter train travels faster so that's the train that must have started in the back. It has to completely overtake the 280 meter train. How many meters does it need to travel from the moment the front of the 520 m train reaches the back of the 280 m train until the back of the 520 m train is at the same spot as the front of the 280 m train?
In other words we want to get from here:
|-------520-------||---280---|
To here:
|---280---||-------520-------|
Of course they'll be on two separate tracks.
So think logically (as you requested). The 520 m train needs to first cover the distance of the 280 m train, which is 280 meters. Now the two trains have their fronts next to each other. So the 520 m train now needs to travel the entire length of ITSELF for the back of it to be where the front currently is. That's another 520 meters.
That's the 520+280 part.
The speeds are given in km per hr so we need to convert 520+280 into km. To do that, just multiply by 0.001.
And finally, how do you get time from a rate and a distance? Remember that r * t = d, so t = d / r.
We have d = (520 + 280) * 0.001. We have the rate also. The difference in rates is 8 km per hr. So the 520 m train is traveling at 8 km per hr relative to the 280 m train.
The answer is thus [(520 + 280) * 0.001] / 8.
