A train 1 mile long travels at 30 mph. It enters a tunnel 1 mile long at 4pm.?

At what time does the end of the train emerge from the tunnel? A train a mile and a half long takes a minute and a half to go through a tunnel a mile and a half long. How fast is it going?
How would you set up the math problem?

4.04pm
120mph

60 minutes in an hour so the train goes half a mile per minute. , so the rear of the train enters the tunnel at 4:02pm if the front enters at 4:00. Therefore the end of the train emerges at 4:04pm

The mile-and-a-half long train is going 3 miles in one minute for it to clear the tunnel, so 3 miles per minute breaks down to 120 miles per hour

4.04pm

At 30mph it takes 2 minutes to cover 1 mile, so it will take 2 min for the front to get to the end and another 2 min for the rest to get out.

not sure about 2nd part

The train needs to travel two miles (one mile into the tunnel and one mile out of the tunnel for the end to emerge). 30mph is one mile every two minutes (60mph 1:1, mile:min. therefore 30mph 1:2) The answer is: 2 miles X 2 min/mile - 4 minutes. (the miles units cancel out) 4:04 PM.

1. Both the train and the tunnel are 1 mile long, so in other words, how long does it take the train to travel 2 miles?
distance travelled = speed * time taken

t = d / s = 2 / 30 = 0.06666... hours = 4 minutes

The train exits the tunnel at 4.04pm


2. Train takes a minute and a half to travel 3 miles.

1.5 min = 3/120 hours

s = d / t = 3 / (3/120) = 120 mph

4 min for whole train to be out
120 mph

OK this is easy.

The train is a mile long. The tunnel is a mile from opening to opening. We'll say for argument's sake the tunnel openings face W and E, and the train is travling easterward.

If the train's engine enters Western Opening of the tunnel and was moving at ONE mile per hour, it would take TWO hours for the last car, or caboose, of the train to emerge from the Eastern Opening of the tunnel. IF the train moves at ONE mile per hour and the tunnel and train is one mile long, it will take the train ONE HOUR to transit the tunnel and one more HOUR for it to pull it's caboose out of the tunnel.

Now let's speed things up a bit.

The train is moving at 30 miles per hour. That means that in 60 minutes, the train will cover 30 miles. Or more precisely, it takes the train TWO MINUTES to cover ONE MILE.

The train's engine enters the western opening of the tunnel (the train is eastbound) at 4 pm. It will have transited the tunnel so that by 4:02 pm the engine will be emerging from the eastern opening the tunnel. The train still has to pull one mile of train thru the tunnel, and that mile will take two more minutes to cover. So at 4:04 pm, the last car of the train will emerge from the tunnel.

The answer is 4:04 pm.
I hope my explanation helped you understand this.

As for question #2, let's take a look:

When you say 'go thru the tunnel' does that mean just the engine enters and then emerges at the other side, or is it like the 'entire train' thing that means that the engine and train behind it enters the tunnel, and 90 seconds later (a minute and a half) the LAST car exits the tunnel or is it only the engine? This is important to know because the answer will be different. I'll try it both ways:

The engine in #2 will have to travel a total distance of 3 miles from when it first enters the tunnel to transit the tunnel and pull the last car out of the tunnel (1.5 miles for the tunnel, and then the extra 1.5 miles for the train). So it travels 3 miles in that minute and a half (90 seconds) to get thru the tunnel and get the last car out. That means that the train is traveling 1 mile in 30 seconds, 2 miles in 60 seconds, and 3 miles in 90 seconds. So at 2 miles a minute, that is 120 miles per hour (2 miles x 60 seconds per mile).

So if the train has to PULL its entire length thru the tunnel in question #2, that is if it has to enter the tunnel, transit the tunnel, and then pull the entire 1.5 mile of train out of the tunnel in 1.5 minutes, it is traveling at 120 mph.

IF, however, your definition of 'exiting' the tunnel is just the engine emerging from the eastern side of the tunnel, then it travels that 1.5 miles in 1 minute, which if you multiply it by 60 to get mph, it's 1.5 miles x 60 minutes = 90 miles per hour.

It all depends on what you mean by 'exit' the tunnel. I assume that it is similar to question one one in that the train must EXIT the tunnel completely to be considered to be exited (last car in the train). So the answer would be 120 mph.

If, on the other hand, it's just opening to opening (1.5 mile) then the answer is 90 mph.

q1
2*1/30 = 1/15 hour = 4 minutes
answer
= 4 : 04 pm

q2
2*1.5 / v = 1.5/60
v = 2*60 = 120 mph