Question

Suppose two trains, say A and B are initially 125 miles apart on the same east-west track. Train A is initially to the west of train B. Train A begins to head due east at 25 mph, and train B begins to head due west at 20 mph. To the nearest minute, how long will it take for the two trains to collide?

Answer 1

`167\ \text{minutes}\text{ or }166\ \text{minutes}\ \text{and}\ \text{40}\ \text{seconds}`

Explanation:

Distance between the two trains is 125 miles.

So, when they will collide they would have covered a distance of 125 miles together.

The time that will pass for both the trains will be same but the distances covered will be different as their speeds are different.

`\text{Distance}=\text{Speed}* \text{Time}`

`25t+20t=125\\\Rightarrow t=(125)/(45)\\\Rightarrow t=(25)/(9)\ \text{hours}=(25)/(9)* 60* 60=10000\ \text{s}=166.67\ \text{minutes}\\\approx 167\ \text{minutes}\\=166\ \text{minutes}\ \text{and}\ \text{40}\ \text{seconds}`

`167\ \text{minutes}\text{ or }166\ \text{minutes}\ \text{and}\ \text{40}\ \text{seconds}`