, 2020

Solution 1

There are 60 minutes in 1 hour, and so there are $60+52=112$ minutes in 1 hour 52 minutes.

If Emil’s race time was 54 minutes, then Olivia’s race time was 4 minutes more, or 58 minutes.

In this case, their race times total $54+58=112$ minutes, as required.
Therefore, it took Olivia 58 minutes to run the race.

Solution 2

As in Solution 1, the total of their race times is 112 minutes.

If Emil’s race time was 4 minutes more, then his race time would be equal to Olivia’s, and the total of their race times would be $112+4=116$ minutes.

If their race times are equal and total 116 minutes, then they each finished the race in $116\div2=58$ minutes.
Therefore, it took Olivia 58 minutes to run the race.

The $y$-coordinates of points $P(15,55)$ and $Q(26,55)$ are equal.

Therefore, the distance between $P$ and $Q$ is equal to the positive difference between their $x$-coordinates, or $26-15=11$.

Similarly, the $x$-coordinates of points $R(26,35)$ and $Q(26,55)$ are equal.

Therefore, the distance between $R$ and $Q$ is equal to the positive difference between their $y$-coordinates, or $55-35=20$.
Since $PQ=11$ and $RQ=20$, the area of rectangle $PQRS$ is $11\times20=220$.