Question

A bicycle 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?

Answer 1

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 !