I'm leaving on a Caltrain

First, realize that since his train is moving at an equal speed in the opposite direction of the passing trains, the actual interval between each train at a stationary point is 40 min .

For example, lets say two persons are 4 steps away from each other. If one were to stay stationary, then it would take 4 steps for the other person to reach the other.

However, if they were both to take a step towards each other, then after 2 steps they would reach each other.

Once we know the interval between each train on a stationary location, it is easy to find how many arrive in San Francisco.

$8\text{ hrs} \cdot 60 \text{ min} = 480 \text{ min}$

$\frac{480 \text{ min}}{40 \text{ min}} = \fbox{12}$

Since there are $60$ minutes per hour, there are three $20$ -minute intervals per hour. Since the train ride lasts $8$ hours, there are $3 \frac{intervals}{hour} \times 8 hours = 24$ intervals. At each interval along Calvin's way, the train he passes has the amount of time left in Calvin's trip to make it to San Francisco. This implies that after Calvin passes half of the total time allotted, any train that he meets will not be able to make it entirely to San Francisco in time (this is attributed to the fact that all trains run at equal speeds and depart at fixed regular intervals). Thus, the number of intervals is restricted to half of the total, as stated. This leads us to $12$ intervals and thus $\boxed{12}$ trains arriving at San Francisco station by the end of the $8$ hours.

Nos 20 minutos iniciais, o trem de Calvin passa pelo primeiro trem cujo sentido é San Francisco; no entanto, esse trem chegará àquela estação 20 minutos depois, ou seja, 40 minutos após a partida de Calvin. Seguindo o mesmo raciocínio para o próximo trem concluímos que a cada 40 minutos chega um trem em San Francisco.

Daí, apliquemos uma regra de três simples:

40 minutos --------------------------- 1 trem

8 horas -------------------------------- x

$\frac{40}{8 \cdot 60} = \frac{1}{x} \\\\ 40x = 480 \\\\ \boxed{x = 12}$

8×60÷(2×20)=12

We know that the train are running on same speeds therefore the train which meet the train of calvin after 20 minutes will reach the san francisco after 20 mins. which means 40 minutes after the departure of calvin's train. there fore trains which meet the cal's train 4 hours after the departure of cal's train will reach the san francisco after 8 hrs. of the departure

hence the no. of trains in 4 hrs are 4*60/20 =12 trains

Okay we know that each train travels at the same speed, and departs in fixed regular intervals.

Going forwards Calvin see's a train passing every 20 minutes, However if one of the trains were to be still, then Calvin would see a train pass every 40 minutes.

Therefore we know that each train departs every 40 minutes.

Because we know that a train departs every 40 minutes, and that the question is asking for the amount of trains that arrive in 8 hours (480 minutes),

we do 480 divided by 40, and get $\boxed{12}$

In 480 minutes, 12 trains depart and 12 trains arrive.

In 8 hours ,24 trains will reach san .but since calvin is crossing every train ,so answer will be half that is 12 trains

Since Calvin sees a train approaching him every 20 minutes , and since speed of his train is same as that of the approaching train , actually a train leaves Los Angeles every 40 minutes ; therefore total no of trains reaching San Fransisco in 8 hours ie, 480 minutes is 480/40 = 12

Since Calvin is in the train reference frame, and he sees that after every 20 mins a train passes with double speed than what is the speed of the trains from ground frame , thus actually the interval between trains is 40 mins. Divide 8 hrs by 40 mins to get 12...

Actually it is said that they are crossing for every 20 min(as they have equal speeds they have to cross at mid point itself) That is for every 40 min a train will be arrived to san francisco ie.no.of trains in 8 hrs = 8*60/40=12