Alice is in a 20-km running race. She always runs the first half at an average speed of 2 km/h faster than the second half.
a) Let x represent her speed in the first half. Determine a simplified expression in terms of x for the total time needed for the race.
b) If alice runs the first half at 10km/h, how long will it take her to run the race?

If x is the rate at which she runs the second half, then x+2 is the rate she runs the first half.

Her average velocity is then

\frac{2x(x+2)}{x+(x+2)}

If x=10, what is her average rate?

Use that to find how long it takes her to run 20 km at that rate.