betty,cathy,isabel,lani,alma,and ursula ran an 800meter race. alma beat isabel by 7 meters. ursula beat betty by 12 meters. alma finished 5 meters ahead of lani but 3 meters behind ursula. cathy finished halfway between the 1st and last girl. In what order did they finish? what were the distances between each girl?
so confused please help
It will not be complicated if we write down the information mathematically.
Let the initial of each person represent the distance in metres ahead of the last athelete.
Then according to the question:
A-I = 7
U-B = 12
A-L = 5
U-A = 3
Disregard Cathy for the moment.
We can tell that Ursula is ahead of everyone, and Alma is second, since there is only ursula ahead of her. Since A-L=5 and A-I=7, we conclude that Lani is ahead of Isabel.
The order is thus, after applying the distances
U=12
A=9
L=4
I=2
B=0
Now we can insert Cathy being (U+B)/2=6, between Alma and Lani.
What strategy did you use? (the name of the strategy)
Let's break down the given information:
1. Alma beat Isabel by 7 meters.
2. Ursula beat Betty by 12 meters.
3. Alma finished 5 meters ahead of Lani but 3 meters behind Ursula.
4. Cathy finished halfway between the 1st and last girl.
Based on this information, let's solve this step by step:
Step 1: Find the halfway point between the 1st and last girl.
Since there are six runners, the halfway point is between the 3rd and 4th position. Therefore, Cathy finished in the 3rd position.
Step 2: Determine the order of the runners.
- From the previous step, we know Cathy finished 3rd.
- Ursula beat Betty by 12 meters, so Betty finished 4th and Ursula finished 5th.
- Alma finished 5 meters ahead of Lani but 3 meters behind Ursula, so Alma finished 6th and Lani finished 2nd.
- This means Isabel finished 1st.
Therefore, the order of the runners is:
Isabel - 1st
Lani - 2nd
Cathy - 3rd
Betty - 4th
Ursula - 5th
Alma - 6th
Step 3: Calculate the distances between each girl.
- Isabel finished first, so there is no distance to calculate before her.
- Isabel finished 7 meters ahead of Alma.
- Alma finished 5 meters ahead of Lani.
- Lani finished 12 meters ahead of Ursula.
- Ursula finished 3 meters ahead of Betty.
- Betty finished 6 meters ahead of Cathy.
Therefore, the distances between each girl are:
Isabel - Alma: 7 meters
Alma - Lani: 5 meters
Lani - Ursula: 12 meters
Ursula - Betty: 3 meters
Betty - Cathy: 6 meters
To solve this problem, let's analyze the given information step by step:
1. We know that Alma beat Isabel by 7 meters. Let's assume Alma finished ahead of Isabel. This means Alma finished with a lead of 7 meters.
2. We also know that Ursula beat Betty by 12 meters. Let's assume Ursula finished ahead of Betty. This means Ursula finished with a lead of 12 meters.
3. Additionally, we know that Alma finished 5 meters ahead of Lani but 3 meters behind Ursula. This information is a bit more complicated. Let's break it down:
- Alma finished 3 meters behind Ursula. So, let's consider that Alma finished 3rd and Ursula finished 2nd.
- Alma finished 5 meters ahead of Lani. So, let's consider that Lani finished 4th.
4. Now, we have four runners assigned to their positions: Ursula (2nd), Alma (3rd), Lani (4th), and Isabel. By process of elimination, Isabel must have finished 5th.
5. Lastly, we are told that Cathy finished halfway between the 1st and last girl. Since Ursula finished 2nd and Isabel finished 5th, Cathy must have finished 3rd or 4th. However, since Alma finished 3rd, Cathy must have finished in the 4th position.
Based on this analysis, the final order is as follows:
1st - Ursula
2nd - Betty
3rd - Alma
4th - Cathy
5th - Lani
6th - Isabel
Now, let's calculate the distance between each pair of girls:
- Distance between Ursula and Betty: 12 meters (as Ursula beat Betty by 12 meters).
- Distance between Betty and Alma: Unknown (not given in the information).
- Distance between Alma and Cathy: Unknown (not given in the information).
- Distance between Cathy and Lani: Unknown (not given in the information).
- Distance between Lani and Isabel: Unknown (not given in the information).
Unfortunately, we cannot determine the exact distances between each girl as some of the information is still missing.