Help me with this homework question.---**Question Number:** 8
**Question Stem:**
The diagram shows three motorway service stations P, Q and R on a map.
**Diagram Description:**
* Type: Line diagram representing distances on a map.
* Elements:
* Three points labeled P, Q, and R are shown in a horizontal line, ordered from left to right (P, then Q, then R).
* A segment between P and Q is marked with a double-headed arrow and labeled "8 cm".
* A segment between Q and R is marked with a double-headed arrow and labeled "16 cm".
**Additional Information:**
The map has a scale of 1 cm = 4 km.
**Task:**
Work out the real distance from P to R.
**Answer Unit:**
km
**Marks:**
(Total for Question 8 is 3 marks)
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In this problem, we have a map showing three motorway service stations labeled P, Q, and R. The distance from P to Q on the map is 8 centimeters, and the distance from Q to R is 16 centimeters. The map has a scale where 1 centimeter represents 4 kilometers in real life. We need to calculate the actual distance from P to R in kilometers.
The first step is to find the total distance from P to R on the map. We know that the distance from P to Q is 8 centimeters, and the distance from Q to R is 16 centimeters. To find the total distance from P to R, we add these two distances together: 8 centimeters plus 16 centimeters equals 24 centimeters. So, the total distance from P to R on the map is 24 centimeters.
Now that we know the total distance on the map is 24 centimeters, we need to convert this to the real-world distance using the given scale. The scale tells us that 1 centimeter on the map represents 4 kilometers in real life. To find the real distance, we multiply the map distance by the scale factor. So, 24 centimeters multiplied by 4 kilometers per centimeter equals 96 kilometers. Therefore, the real distance from service station P to service station R is 96 kilometers.
Let's summarize what we've done to solve this problem. First, we found the total distance on the map by adding the distance from P to Q and the distance from Q to R. This gave us 8 centimeters plus 16 centimeters, which equals 24 centimeters. Next, we converted this map distance to the real-world distance using the scale of 1 centimeter equals 4 kilometers. We multiplied 24 centimeters by 4 kilometers per centimeter to get 96 kilometers. Therefore, the real distance from service station P to service station R is 96 kilometers.