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.

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.