Question

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 1

The speed in running is 10 mph and speed in biking is 16 mph

Solution:

Given that, Cruz is training to compete in a triathlon

He left his house at 6:00 and ran until 7:30

Time taken for running = 1.5 hours

Then he rode his bike until 9:45

7: 30 to 9: 45 is biking time

Time taken for biking = 2.25 hours

He covered a total distance of 51 miles

Total distance = 51 miles

Let "x" be the speed in running

His speed when biking was 1.6 times his speed when running

Speed in biking = 1.6x

Total distance = distance in running + distance in biking

The distance is given by formula:

$distance = speed \times time$

Therefore,

$Total\ Distance = x \times 1.5 + 1.6x \times 2.25\\\\51 = 1.5x + 3.6x\\\\5.1x = 51\\\\x = 10$

Thus speed in running is 10 miles per hour

Speed in biking = 1.6x = 1.6(10) = 16

Thus speed in running is 10 mph and speed in biking is 16 mph