Suppose two bicyclists start at the same location. The first bicyclist rides due north and the other rides
due west. Find the speed that each bicyclist rode in
miles per hour if they are 8V2 miles apart after riding
for 2 hours at the same speed

  4 mi/h

Step-by-step explanation:

The distance between the cyclists is the hypotenuse of an isosceles right triangle. The hypotenuse is √2 times the length of the legs in such a triangle, so each cyclist must have ridden 8 miles in 2 hours.

Their speed is (8 mi)/(2 h) = 4 mi/h.

Additional comment

Consider an isosceles right triangle with leg lengths 1. Then the Pythagorean theorem tells us the length of the hypotenuse is ...

  c² = a² +b² . . . square of hypotenuse is sum of squares of legs

  c² = 1² +1² . . . . both legs are 1 in our example triangle

  c² = 2

  c = √2

That is, the hypotenuse is √2 times the leg length.

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