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