Question

A subway train makes six stops of equal length during its 21 km run. The train is actually moving for 20 min of the trip. At most how long can the train remain at each station if the average speed for the trip, including stops, is to be at least 36 km/h.

Answer 1

Interesting question! Let me work it out on paper...

Answer 2

Average Speed = Distance / Time Let total time stopped be x hrs

Answer 3

Let t be the total amount of time.
We know that t = 20 min + x min

Let v be the average velocity along the whole trip,
we know that v =36km/h

Let d be the total amount of distance traveled,
we know that d = 21 km

We also know that d = v*t

Can you solve this? It's a simple algebraic equation but you have to watch out for unit conversions.

Answer 4

i got 21=36(20+x) but i don't think this is correct

Answer 5

You have written distance = speed * time and this is the same as

speed = distance/time so now just solve for x...

Answer 6

Right. But don't forget the units in your equations. It is very important!

Answer 7

I solved it before but I threw my paper away so I can't check the solution for you, but I remember the unit conversions where the most tricky part, because it's easy to forget :)

Answer 8

but when i solved it i got 21= 720 + 36x
which is 699=36x
so x would be 19.4166667

Answer 9

Your time has to be in hours....

Answer 10

Remember I said "Let total time stopped be x hrs"

Answer 11

Or you couold convert your speed to km per minute but that's more complicated...

Answer 12

20 minutes = 1/3 hours

Answer 13

but i still don't understand how you would convert the whole thing. what would be the equation i would solve?

Answer 14

you had the right equation but you put (20 + x) for the time.

You have to put (1/3 + x)

Answer 15

9= 36x
x= 1/4 (15 min)
but i looked in the book and the answer said at most 2 and 1/2 minutes.

Answer 16

but i don't get how to get that answer

Answer 17

x is the total time stopped ie all 6 stops and
15/6 = 5/3 or 1 and 2/3 minutes per stop
I don't know how they are calculating the "average" I also don't know why they are saying "at most"

Answer 18

but i still don't understand how you get the answer

Answer 19

You had 21=36(20+x) but time should be in hours so

21 = 36(1/3 +x) = 12 + 36 x so

x = 9/36 = 174 hour or 15 minutes...