Question

Suppose two bicyclists start at the same location.

The first bicyclist rides due south and the other rides due east. Find the speed that each bicyclist rode in miles per hour if they are 12√2 miles apart after riding for 1.5 hours at the same speed.

Answer 1

Refer to the image attached.

Answer 2

8 Mph

Explanation:

We can solve this problem by using the Pythagorean theorem, which relates the lengths of the sides of a right triangle. Let's call the speed of the first bicyclist "v1" and the speed of the second bicyclist "v2". After 1.5 hours of riding, the first bicyclist has traveled 1.5v1 miles to the south, and the second bicyclist has traveled 1.5v2 miles to the east. The distance between them is the hypotenuse of a right triangle with legs of length 1.5v1 and 1.5v2:

c^2 = (1.5v1)^2 + (1.5v2)^2

where c is the distance between the two bicyclists, which is given as 12√2 miles. Substituting and simplifying, we get:

(12√2)^2 = (1.5v1)^2 + (1.5v2)^2

288 = 2.25v1^2 + 2.25v2^2

128 = v1^2 + v2^2

We also know that the two bicyclists are traveling at the same speed, so v1 = v2. Substituting this into the equation above, we get:

128 = 2v1^2

v1^2 = 64

v1 = √64 = 8

Therefore, each bicyclist is traveling at a speed of 8 miles per hour.