Final answer:
By applying the Pythagorean theorem to the right-angled triangle formed by Joey, Layla, and Ruth's positions on the bus, we calculate that Layla is 17 feet from Ruth. The provided options do not include 17 feet, suggesting a possible error in the options.
Step-by-step explanation:
The question asks us to find the distance between Layla and Ruth, given Joey's position in relation to both. Let's visualize this scenario with Joey, Layla, and Ruth sitting on the bus. Since Joey is 15 feet behind Layla and 8 feet to the left of Ruth, this forms a right-angled triangle between Joey, Layla, and Ruth, with Joey's position as the right angle's vertex.
To find the distance between Layla and Ruth, we can use the Pythagorean theorem (a2 + b2 = c2), where a and b are the legs of the triangle and c is the hypotenuse. In this case, Joey's distances from Layla and Ruth will be the legs, and the distance between Layla and Ruth will be the hypotenuse.
Calculating this, we have:
a2 = 152 (Joey behind Layla)
b2 = 82 (Joey left of Ruth)
c2 = a2 + b2
c2 = 152 + 82
c2 = 225 + 64
c2 = 289
c = √289
c = 17
Therefore, the distance between Layla and Ruth is 17 feet, which is not one of the options provided. However, assuming that this is a mistake and option b) should be 17 feet instead of 7 feet, the correct answer would be option b).