Abicycle racer rides from a starting marker to a turnaround marker at 10 m/s. she then rides back along the same route from the turnaround marker to the starting marker at 23 m/s .what is her average speed for the whole race?

             Speed  =  (distance covered)  /  (time to cover the distance)

Whatever the distance is to the turnaround marker, let's call it ' D ' .

             Time to cover a distance  =  (distance)  /  (speed)

             Her time for the first half  =  D / (10 m/s)

             Her time to return   =   D / (23 m/s)

             Her total distance covered  =  2 D

             Her total time to cover the distance  =   (D/10  +  D/23)

                                                                           =  D (1/10 + 1/23)

             Her average speed for the whole race  =  2 D  /  D(1/10 + 1/23) 

                                                                                =      2  / (1/10 + 1/23)

So we have to add those fractions.
The least common denominator is  230 .
     
                   (1/10 + 1/23)  =  ( 23/230  +  10/230)

                                           =      33 / 230  .

              Her average speed for the whole race  = 

                                          2 /  (33/230)

                                      =   2 (230 / 33)

                                      =         13.94 m/s  .  

That was complicated, and I'll admit I don't have a high level of confidence.
BUT ...
I'm not going to spend any moire time on it for 5 points.
SO ...
That's my answer, and I'm stickin with it !

Ithink it is letter b, i may be wrong but i think that is the answer