A freight train departed from A to B at a speed of 66 km / h, and 20 minutes later a fast train, moving at a speed of 90

A freight train departed from A to B at a speed of 66 km / h, and 20 minutes later a fast train, moving at a speed of 90 km / h, passed through B in direction A. How long after leaving A will the freight train meet the fast train if there are 256 km between stations A and B?

Let’s find out what part of an hour is 20 minutes:

60: 20 = 3

That is, the freight train was on the way for 1/3 of an hour before the departure of the passenger train from V. Let us find what distance the freight train covered during this time:

66 * 1 \ 3 = 23

Now let’s calculate how many km are left for the trains to cover after the passenger leaves B:

256 – 23 = 234

It is clear from the conditions of the problem that the trains were moving in opposite directions, that is, towards each other. Consequently, the distance between them decreased at a speed equal to the sum of the speeds of the given vehicles. Let’s find this sum of speeds:

66 + 90 = 156

We divide the remaining distance by the total speed of the trains to find how long it will take, after leaving B of the passenger train, they will meet:

234: 156 = 1.5

That is, before the meeting, the freight train was on the way for 20 minutes and another 1.5 hours, that is, another 1 hour and 30 minutes. Let’s calculate how much he was on the way:

1 hour 30 min + 20 min = 1 hour 50 min

Answer: by the time of the meeting. the freight train was on the way for 1 hour and 50 minutes.