a) Let ∣W1B1∣=a1, ∣W2B1∣=a2, ∣W1B2∣=b1, and ∣W2B2∣=b2.
We are given the following conditions:
1. a1+a2=4
2. b1+b2=8
3. b1+a1=9
4. b2+a2=3
From these conditions, we can derive the following steps:
1. Subtract equation (4) from equation (3):
(b1+a1)−(b2+a2)=9−3
b1+a1−b2−a2=6
2. Substitute a1+a2=4 into the equation:
b1−b2=6
3. From equation (3), solve for b1:
b1=9−a1
4. From equation (4), solve for b2:
b2=3−a2
5. Substitute b1=9−a1 and b2=3−a2 into b1−b2=6:
(9−a1)−(3−a2)=6
9−a1−3+a2=6
6−a1+a2=6
−a1+a2=0
a1=a2
6. Since a1+a2=4 and a1=a2:
2a1=4
a1=2
a2=2
7. Substitute a1=2 into b1=9−a1:
b1=9−2=7
8. Substitute a2=2 into b2=3−a2:
b2=3−2=1
Since b1=7 is greater than the other distances, the extremes are W1 (first white cat) and B2 (second black cat).
The final answer is W1 and B2.