steps question

Test Preparation SAT Preparation
1
  1. Alice and Corrine stand back to back. They each take 10 steps in opposite directions away from each other and stop. Alice then turns around, walks toward Corrine, and reaches her in 17 steps. The length of one of Alice’s steps is how many times the length of one of Corrine’s steps? Note(All of Alice’s steps are the same length and all Corrine’s Steps are the same length).

Why is the answer 10/7 instead of 20/17?

2

Because Alice’s first ten steps are HER step length and have nothing to do with Corrine’s step length, so it will take her 10 steps to get back to where they started. Then the next seven steps represent the distance from “0” (their starting point) to Corrine’s location (10 “Corrine steps” from 0). @BeCambridge

3

Sorry, but does Alice change speed? I thought that she always were faster than Corrine.

4

^ I was going to ‘like’ this, but I’m not sure it’s a joke.

5

Speed isn’t involved. Step length is. How about this:

10a + 10b = 17a

Easier?

6

(a=“one Alice step” and b=“one Corrine step”)

7

( @BeCambridge )

8

So, you are saying that, when they were standing back-to-back, they were 7 feet away from each other? (I interpreted it LITERALLY.)

9

Alice and Corrine started at ‘0’. Alice walked 10 steps from 0, then 10 steps back to 0, so ignore those. Once Alice is back to 0, she takes 7 more steps (10+7=17) to reach Corrine. So, in effect, Corrine never had to leave 0. She took 7 steps to reach Corrine, who took 10 steps to get to the same place. So, Alice’s step-length is 10/7 of Corrines’s

Note: All of Alices steps were the same length, and all of Corrine’s steps were the same length…but they are not equal to one another.

10

@BeCambridge I don’t want to be harsh, but I really don’t understand what you’re saying here. What are feet with regards to this question? When they are standing back-to-back, they are presumed to be next to each other. 2muchquan’s explanation should be very clear and I encourage you to read it completely.