Question

mr. adams took his life sciences learners on an excursion to the madikwe game reserve. they drove from johannesburg to the madikwe game reserve and planned to enter the game reserve at the abjaterskop gate. the map (below) indicates the routes, cities or towns and distances (in kilometers) between the places. route map from johannesburg to the madikwe game reserve use the given information and the route - map to answer the questions that follow. 3.1 give the general direction of the madikwe game reserve from johannesburg. (2) 3.2 explain the shortest route that could be used to drive from johannesburg to the abjaterskop gate. (2) 3.3 calculate the distance between zeerust and swartruggens if the total route distance from rustenburg to the abjaterskop gate is 221.2 km. (3) 3.4 determine the shortest route distance from johannesburg to swartruggens. show all calculations. (2) 9

Explanation:

Step1: Determine general direction

Based on the map and compass direction, the Madikwe Game Reserve is in the north - west direction from Johannesburg.

Step2: Find shortest route to Abjaterskop Gate

From the map, the shortest route from Johannesburg to Abjaterskop Gate is Johannesburg - Pretoria - Rustenburg - Swartruggens - Zeerust - Abjaterskop Gate.

Step3: Calculate distance between Zeerust and Swartruggens

Let the distance between Zeerust and Swartruggens be $x$.
We know the distance from Rustenburg to Abjaterskop Gate is 221.2 km. The sum of distances Rustenburg - Swartruggens (62.4 km), Swartruggens - Zeerust ($x$) and Zeerust - Abjaterskop Gate (88.1 km) is 221.2 km.
So, $62.4 + x+88.1 = 221.2$.
$x=221.2-(62.4 + 88.1)$.
$x = 221.2 - 150.5$.
$x = 70.7$ km.

Step4: Determine shortest route distance to Swartruggens

Route 1: Johannesburg - Pretoria - Rustenburg - Swartruggens: $65.0+129 + 62.4=256.4$ km.
Route 2: Johannesburg - Magaliesburg - Rustenburg - Swartruggens: $70+61.4 + 62.4 = 193.8$ km.
The shortest route distance is 193.8 km.

Answer:

3.1 North - west
3.2 Johannesburg - Pretoria - Rustenburg - Swartruggens - Zeerust - Abjaterskop Gate
3.3 70.7 km
3.4 193.8 km