Question 933374
{{{d}}}= 1/3 of the total route distance, in km, and
{{{3d}}}= the total route distance, in km.
Average time for the whole route ={{{3d/24}}} hours.
The time spent cycling uphill was {{{d/16}}} hours, and
the time spent cycling on level was {{{d/24}}} hours.
So, the time spent cycling downhill must have been
{{{3d/24-d/16-d/24=6d/48-3d/48-2d/48=(6d-3d-2d)/48=d/48}}} hours.
Then, the average speed in km/h cycling uphill for {{{d}}} km in {{{d/48}}} hours was
{{{d/"( d / 48 )"=d(48/d)=highlight(48)}}} .
 
CHECKING:
Let's say that the total route is {{{48*3=144}}} km.
That means {{{48}}} km cycling downhill, at {{{48}}} km/h, during {{{1}}} hour,
{{{48}}} km cycling on level ground, at {{{24}}} km/h, during {{{2}}} hours, and
{{{48}}} km cycling uphill, at {{{16}}} km/h, during {{{3}}} hours,
for a total of {{{48*3=144}}} km covered in {{{1+2+3=6}}} hours,
at an average rate of {{{48*3/6=24}}} km/h.