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