#
Problem
of the Week

Problem
A and Solution

Dog
Walking

## Problem

Petra walks his dog once a day. Most days when Petra walks his dog,
he takes a route that is \(3
\frac{1}{2}\) km long. When it is raining, he does a shorter walk
which is only \(2\) km long.

One week it rained for \(3\) days
and did not rain on the other \(4\) days. How far did Petra walk his dog
that week?

## Solution

On each of the \(3\) days it rained,
Petra walked \(2\) km for a total of
\(2 + 2 + 2 = 6\) km.

On each of the \(4\) days it did not
rain, Petra walked \(3
\frac{1}{2}\) km.

We know that \(3 \frac{1}{2}\) is the
same as \(3 + \frac{1}{2}\), so over
four days, the total distance Petra walked is equal to \(3 + \frac{1}{2} + 3 + \frac{1}{2} + 3 +
\frac{1}{2} + 3 + \frac{1}{2}\).

Collecting the whole numbers and the fractions, we can rewrite this
as \(3 + 3 + 3 + 3 + \frac{1}{2} + \frac{1}{2}
+ \frac{1}{2} + \frac{1}{2}\).

Since \(\frac{1}{2} + \frac{1}{2} =
1\), we can rewrite this as \(3 + 3 + 3
+ 3 + 1 + 1 = 14\) km.

Alternatively, to calculate the distance Petra walked on the days it
did not rain, we can add \(3 \frac{1}{2} + 3
\frac{1}{2} = 7\) km which is how far Petra walked in two days.
So he walked twice as far in four days, which is \(7 \times 2 = 14\) km.

So the total distance Petra walked that week is \(6 + 14 = 20\) km.

Alternatively, we can do the calculation in metres.

Since we know that \(1\) km is equal to
\(1000\) m, then \(\frac{1}{2}\) km is equal to \(500\) m.

So \(3 \frac{1}{2}\) km is equal to
\(3 \times 1000 + 500 = 3500\) m and
\(2\) km is equal to \(2 \times 1000=2000\) m.

This means the total distance Petra walked is equal to \(2000 + 2000 + 2000 + 3500 + 3500 + 3500 + 3500 =
20000\) m, which is \(20\) km.