A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 6 km per hour and the level part at the rate of 9 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 9 km per hour for the entire route?  Choose one.
A) 12  B) 15  C) 18  D) 21  E) 24
Let V be the speed on the downhill section.   Let D be the distance of each of the three equal sections.   Total time T = T1+T2+T3 and 3D/T = 9 km/hour   3D / (D/6 + D/9 + D/V) = 9   1/3 = 1/6 + 1/9 + 1/V   1/V = 1/18 and so V = 18 km/h   The answer is 18.
<result>C</result>
A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 6 km per hour and the level part at the rate of 9 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 9 km per hour for the entire route?