Cruz is training to compete in a triathlon. He left his house at 6:00 and ran until 7:30. Then he rode his bike until 9:45. He covered a total distance of 51 miles. His speed when biking was 1.6 times his speed when running. Find Cruz's biking and running speeds.

Answer: Cruz's biking is 16 miles per hour and his running speed is 10 miles per hour.

Step-by-step explanation:

Let x represent Cruz's speed when running.

He left his house at 6:00 and ran until 7:30. This means that the time spent while running is 1hour 30 minutes = 1.5 hours.

Distance = speed * time

Distance covered while running would be

1.5 * x = 1.5x

Then he rode his bike until 9:45. This means that the time he spent riding his bike is 2hours 15 minutes = 2 hours + 15/60 = 2.25 hours

His speed when biking was 1.6 times his speed when running. It means his speed when biking would be

1.6 * x = 1.6x

Distance covered while riding would be

1.6x * 2.25 = 3.6x

He covered a total distance of 51 miles. Therefore,

1.5x + 3.6x = 51

5.1x = 51

x = 51/5.1 = 10 miles per hour.

His biking speed would be

1.6 * 10 = 16 miles per hour.