#
Problem
of the Week

Problem
C and Solution

Uphill
and Downhill

## Problem

Rory biked \(36\) km up a trail from
his campsite to a lookout point. On the way up, his average speed was
\(9\) km/hr. On the way back down, he
biked faster, with an average speed of \(12\) km/hr. What was his average speed, in
km/hr, for the entire trip?

## Solution

First we calculate the time it took Rory to bike up to the lookout
point and back down to his campsite.

Rory’s \(36\) km ride up to the
lookout point at \(9\) km/hr took \(36 \div 9 = 4\) hrs. Rory’s \(36\) km ride back down to his campsite at
\(12\) km/hr took \(36 \div 12 = 3\) hrs. Thus, the total time
was \(4+3=7\) hrs.

Rory’s trip up to the lookout point and back down to his campsite had
a total distance of \(36+36=72\) km.
Therefore, the average speed for the entire trip was \(72 \div 7 \approx 10.3\) km/h.