Antti entered a $10$-kilometer race. His goal is to finish in one hour. He starts off sprinting, and completes the first $2$ kilometers of the race at an average speed of $12$ kilometers per hour.

To achieve his goal of a one-hour finish time, what average speed must Antti maintain for the last $8$ kilometers of the race?

Enter your answer as a number in decimal form, without units.

Question

Antti entered a $10$-kilometer race. His goal is to finish in one hour. He starts off sprinting, and completes the first $2$ kilometers of the race at an average speed of $12$ kilometers per hour.

To achieve his goal of a one-hour finish time, what average speed must Antti maintain for the last $8$ kilometers of the race?

Enter your answer as a number in decimal form, without units.

mathmale · Answer

Please omit the ' $ ' sign here; it has no relevance to this problem.

The distance to be covered in this race is 10 Km.  The runner's goal is to cover those 10 Km in 1 hour.

He runs at two different speeds, one of which is 12 Km/hr.  Our job is to determine the final speed, which is different from the beginning speed.

Note that distance = rate * time, rate = distance / time, and time = distance / rate.

Use these facts to put together equations relating these variables and constants.