a cyclist travels 12 km on a level road at x km/h and then goes 9 km on a downhill road at 2x km/h. Find her average speed in terms of x.

Question

Average speed = total distance divided by total time

Answer 1

12 km x 1 hr/ x km = 12/x hr

9 km x 1 hr/ 2x km = 4.5/x hr

21/ (12/x + 4.5/x) = 21/(16.5/x) = (21/1)(16.5/x) = 21/1)(x/16.5) = 1.27(x) km/hr

Answer 2

Total distance travelled = 12 km + 9 km = 21 km

If one travels 12 km at x km/h, it takes 12 km/ (x km/h) = 12/x h

Then, one travels 9 km at 2x km/h, for a time of 9 km/(2x km/h)) = 9/(2x) h

Total time is 12/x + 9/(2x) = 33/(2x) h

Then, the rate is 21km/(33/(2x) h) = 42/33 x km/h