Question

Use the Law of Levers to solve the problem. The number of chairs on a ski lift varies inversely as the distance between them. A ski lift can handle 32 chairs when they are 30 feet apart. If 40 chairs were used, how many feet should be left between each pair?

Answer 1

The Law of the Lever looks like this:
\[d_1 \times w_1=d_2 \times w_2\]
In this case, you have both the weights (assuming the weight of the chairs is the same) and you can calculate the lengths (32 chairs 30 feet apart gives you 960 feet). Plug them into your equation to get
\[(960)(32) = 40(d_2)\]
You will need to divide your number by 40 at the end to see how much space should go between EACH pair.

Answer 2

37.2 feet?

Answer 3

37.5 * @jabberwock

Answer 4

Because there are more chairs now, the distance between the chairs must be smaller than before right?

Answer 5

yeah

Answer 6

24?

Answer 7

You divided by 30 at the end instead of 40, I think...

Answer 8

wait so its not 24

Answer 9

its 32

Answer 10

At the end, you have 40 chairs instead of 32. In order to find out how much of that total space should be between them, you have to divide by 40.

Answer 11

37.5

Answer 12

960(32) is 30720
\[30720=40(d_2)\]
Divide both sides by 40 to get 768 as the total length.
But you have 40 chairs, which means that you will have an equal length between each chair (divide by 40), giving you 19.2 feet.

Answer 13

i got 19.8

Answer 14

What seraphic_topaz was saying up above was that 37.5 couldn't work, because if you have more chairs, you would need to have less space between them, not more space.

Answer 15

I tried it again and got 19.2.

Answer 16

Ok, this approach does not seem intuitive. So I take 19.2 x 40 and compare that to 32 x 30. The latter is bigger! So the skilift shrinks somehow? Isn't that how big the lift is must be a constant? And then we just do: more chairs ==> less space; less chairs ==> more space.

Answer 17

Hmm, you might be right. I interpreted the problem as the motor being the limiting factor (only being able to handle a certain amount of weight) and trying to set up the ski lift accordingly in the first place (rather than for a preexisting ski lift). I think I may have made the problem more complicated than what they were asking for.

Answer 18

@allie22, sorry, that explanation I gave was probably wrong. 24 is probably the right answer. I'm not 100% sure about how to interpret the problem though, because it says to use the Law of Levers, which deals specifically with weight and length.

Answer 19

I can definitely see the motor being the limiting factor.