Run!

Algebra Level 2

Miranda trained consistently, so that she can finish a race in an hour. During the race, she ran at the speed of 8 km/h. However, upon reaching the halfway point of the race, she realized that she needed to run faster so she increased her speed to 10 km/h. Assuming she reached her goal just on time, the length of the race can be written as $$\frac{a}{b}$$ km, where a and b are coprime integers, find a + b.

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