An escalator moves up at a constant rate. Chloe takes 90 steps to walk down the escalator. Jacob takes 45 steps to walk up the escalator. Given that Chloe walks 3 times as fast as Jacob, how many steps has the escalator?
The answer is 72 and google has an explanation but I don’t understand it.
Thanks
#Escalator speed/ratio problem
half willow
brave frostBOT
half willow
<@&286206848099549185>
vagrant mica
using ratios we can do something like
ratio of escalator steps = ratio of time
Remember this only works when escalator speed is constant (which is generally the case for escalator problems).
- Find the number of steps the ESCALATOR takes for each case
- Find the time for the escalator in each case
- Set their ratio equal
Let x = number of steps on the escalator
Chloe takes 90 steps to walk down while escalator takes 90-x "walking" up. (if this isnt obvious to you we can do the following: let k be the number of steps the elevator walks up. 90 = x+k ==> k = 90-x).
Jacob takes 45 steps to walk up while the escalator takes x-45 steps to move up too. (again if this isnt obvious, x = 45+k ==> k = x-45).
==> the ratio of the steps is (90-x)/(x-45)
Now we need to find the ratio of time which is distance/speed.
For the 1st case, chloe takes 90 steps and her speed lets say her speed is 3r.
Her time would be 90/(3r) = 30/r. Notice that this time is also the time for the escalator.
Similarily for the 2nd case, jacob takes 45 steps and lets say that his speed is r.
HIs time would be 45/r.
Now the ratio of their time is (30/r)(45/r) = 30/45 = 2/3.
Now set the ratios equal:
(90-x)/(x-45) = 2/3
3(90-x)=2(x-45)
270-3x=2x-90
5x=360
x=72
lol its been 1 month since your question was posted lmao