Question

The tram at Valley View Ski Resort can transport 5000 people in 6 hours. Using the chairlift and tram, 5000 people can be brought to the top in 2 hours. If the tram breaks, how long will it take the chairlift to bring 5000 to the mountaintop? @Calculus1

Answer 1

what the heck kind of problem is this?

Answer 2

I believe its math, but my friends need help on this and I'm not sure how to solve it.

Answer 3

i mean we can do it, but it is not your usual calc kind of problem. just need the rate for each

Answer 4

i think its a work rate problem...

Answer 5

yeah, my friend is in a non-cal math then me, lol. Right now in my calculus class were doing sigma notation

Answer 6

i think the answer is
\[\frac{11}{6}\] but i am not confident so let me check

Answer 7

could you show the work on how to work

Answer 8

the problem

Answer 9

ok let me see if i can write something that make sense. @simon if you have a better explanation please jump in

Answer 10

first of all forget the 5000, because that is a red herring. it is 5000 all the way across, so just think of it as 1, as in one job

Answer 11

@satellite73 I got a different answer: 3 hours

Answer 12

you know the rate of the tram is
\[\frac{1}{6}\] because it carries one sixth of the people per hour. so lets put the rate of the chair lift as R

Answer 13

yeah i think i was wrong

Answer 14

so their combined rate is
\[\frac{1}{6}+R\] and you also know that it takes 2 hours to complete one job, so you know
\[(\frac{1}{6}+R)\times 2=1\] and now we can solve for R

Answer 15

rate of what? I thought of it as the rate\[\frac{dP}{dt} = \frac{5000}{6}\]

Answer 16

I think it's not a good idea to forget about the number 5000

Answer 17

and so you get just what victorana said,
\[R=\frac{1}{3}\] meaning it does one third of the job in an hour, or one job in 3 hours

Answer 18

you can work with the 5000 all the way across if you want, but it is 5000 in every spot. so just make the 5000 a 1 to compute. still get the same thing

Answer 19

just like all those problems that say
"bill can paint the house if 4 hours, joe can paint it in 6 hours, how long if they work together?" just make the job a 1 and forget about how many square feet they are painting

Answer 20

Well I'm not pretty sure that your idea it's ok, but it solves the problem. I have to think!

Answer 21

I got it, that was very clear! Thanks!

Answer 22

i am just replacing 5000 by "all the people"

Answer 23

yw, sorry it took a while

Answer 24

Thanks!

Answer 25

yw, sorry if the explanation was not so clear, i got off on a false start. forgot that i should set
\[(\frac{1}{6}+R)\times 2 = 1\]