Question

Chase trained for 5 hours yesterday. He ran 6 miles and then biked 24 miles. His biking speed is 10 mph faster than his running speed. What is his running speed?

Answer 1

Chase’s running speed can be determined by setting up an equation where x is his running speed, and solving for x in the equation 6/x + 24/(x + 10) = 5, since he trained for 5 hours total.

Step-by-step explanation:

To solve for Chase’s running speed, let’s denote the running speed as x miles per hour (mph). Consequently, his biking speed would be x + 10 mph. Since Chase trained for a total of 5 hours, we need to create two equations based on the distances and the corresponding speeds. For running 6 miles:

Time running = Distance / Speed = 6 / x hours

For biking 24 miles:

Time biking = Distance / Speed = 24 / (x + 10) hours

Since the sum of both times is equal to 5 hours:

6/x + 24/(x + 10) = 5

We can solve this equation by finding a common denominator and setting up a quadratic equation that we can solve for x. Once we find the value of x, that will represent Chase’s running speed. Assuming Chase’s speeds are similar to typical runners, we can note that some runners run at speeds of 7.5 mph or less while others run faster.