Recall that a raisin cake is sometimes used to imagine how an expanding universe behaves. Suppose you are in a uniformly expanding raisin cake, sitting on Raisin A, looking at Raisin B, 2 cm away from you. Raisin B is moving away from you at 1 cm/sec. At the same time, you observe another Raisin C, which is moving away from you at 3 cm/sec. How far away is Raisin C from Raisin A?
A)2/3 cm
B)3/2 cm
C)6 cm
D)3 cm
E)impossible to say

Question

Quizplus · Accepted Answer

In the expanding raisin cake model, the distance between any two raisins increases proportionally to their initial distance. Therefore, the ratio of the distances between raisin A and B and raisin A and C will remain constant over time. We can set up the following proportion:

distance between A and B : distance between A and C = 2 cm : x

where x is the distance between A and C. We know that raisin B is moving away from us at 1 cm/sec, so after time t, the distance between A and B will be 2 + t cm. Similarly, the distance between A and C will be x + 3t cm. Therefore, we can set up another proportion:

(2 + t) cm : (x + 3t) cm = 2 cm : x

Cross-multiplying and simplifying, we get:

2x + 6t = 2(x + 3t)
2x = 6t
x = 3t

So the distance between raisin A and C is always three times the distance between raisin A and B. Therefore, if raisin B is currently 2 cm away from raisin A, raisin C must be 6 cm away from raisin A. The answer is C).

Recall That a Raisin Cake Is Sometimes Used to Imagine