A cyclist rides his bicycle over a route which is 1/3 uphill, 1/3 leve

Responding to a pm:

There are two problems with using the formula given on my blog on this question:

1. There are three different speeds which you need to average out.
2. The weights in case of speed is 'time taken' not distance traveled. Explained here: https://anaprep.com/arithmetic-weights- ... d-average/

In case of three speeds, you can simply use the formula: Cavg = (C1*W1 + C2*W2 + C3*W3)/(W1 + W2 + W3)

Weight in case of speed is 'time taken'

Hence, Avg Speed = Total distance / Total time (which we know)

In this question, I would like to assume that the total distance is 48*3 such that the distance traveled in each leg of the journey uphill, level and downhill is 48 miles (you can assume it to be something else or x)

Time taken to go uphill = 48/16 = 3 hrs
Time taken on level = 48/24 = 2 hrs
Time taken to go downhill = 48/d

Avg Speed = 24 = 48*3/(3 + 2 + 48/d)
48/d = 1
d = 48 miles/hr

You can also look at it in another way - A Shortcut:

Speed on level plain is 24 miles/hr and average speed is also 24 miles/hr. So we can just ignore the level plain since it is at the average.
We need to average out the rest of the journey to 24 miles/hr. Again, assuming that distance of each leg is 48 miles,

24 = 48*2/(3 + 48/d)
d = 48 miles/hr