Suppose the cyclist travels for a total time of t hours.
For 20 min = 1/3 hr, the cyclist does not move.
Over the remaining (t - 1/3) hr, the cyclist is moving at a constant speed of 22.0 km/hr, so that the cyclist would travel a distance of
x = (22.0 km/hr) • ((t - 1/3) hr) ≈ (22.0 km/hr) t - 7.33 km
If the cyclist's average speed over the total time t was 17.5 km/hr, then by the definition of average speed,
17.5 km/hr = x / t
Replace x with the distance expression from earlier:
17.5 km/hr = ((22.0 km/hr) t - 7.33 km) / t
Solve for t :
17.5 km/hr = 22.0 km/hr - (7.33 km) / t
(7.33 km) / t = 4.5 km/hr
t = (7.33 km) / (4.5 km/hr)
t ≈ 1.62963 hr
Then the distance the cyclist traveled must have been
x ≈ (22.0 km/hr) (1.62963 hr) - 7.33 km ≈ 28.5 km
and so the answer is A.
Alternatively, as soon as you arrive at
17.5 km/hr = x / t
you can instead solve for t in terms of x, then plug that into the distance equation.
t = x / (17.5 km/hr)
then
x ≈ (22.0 km/hr) (x / (17.5 km/hr)) - 7.33 km
x ≈ 1.25714 x - 7.33 km
0.25714x ≈ 7.33 km
x = (7.33 km) / 0.25714 ≈ 28.5 km