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 !
