A car and a bus travelled along the same route from Johor to Kuala Lumpur. They left. Johor at the same time. They did not change their speeds throughout the journey.The car reached Kuala Lumpur after 4 hours but the bus had travelled only 5/8 of its journey. The bus travelled at a speed that was 30km than the car. a) Find the distance between Johor and Kuala Lumpur. b) Find the speed of the car

Let's solve the problem step by step.

### Step 1: Define Variables
Let:
- \( d \) be the distance between Johor and Kuala Lumpur in kilometers.
- \( v_c \) be the speed of the car in km/h.
- \( v_b \) be the speed of the bus in km/h.

### Step 2: Write the Equations

From the problem, we know the following:
1. The car reaches Kuala Lumpur in 4 hours.
   \[
   d = v_c \times 4
   \]

2. The bus travels only 5/8 of the journey in 4 hours.
   \[
   \frac{5}{8}d = v_b \times 4
   \]

3. The bus traveled at a speed that was 30 km/h less than the car.
   \[
   v_b = v_c - 30
   \]

### Step 3: Substitute and Solve

#### From Equation 1:
   \[
   d = 4v_c
   \]

#### From Equation 2, solve for \(v_b\):
   \[
   \frac{5}{8}d = 4v_b
   \]
   \[
   v_b = \frac{5}{32}d
   \]

#### Substitute \(d = 4v_c\) into \(v_b = \frac{5}{32}d\):
   \[
   v_b = \frac{5}{32}(4v_c) = \frac{20}{32}v_c = \frac{5}{8}v_c
   \]

#### Substitute \(v_b = v_c - 30\) into \(v_b = \frac{5}{8}v_c\):
   \[
   \frac{5}{8}v_c = v_c - 30
   \]
   \[
   v_c - \frac{5}{8}v_c = 30
   \]
   \[
   \frac{3}{8}v_c = 30
   \]
   \[
   v_c = 30 \times \frac{8}{3} = 80
   \]

So, the speed of the car, \( v_c \), is 80 km/h.

### Step 4: Find the Distance
   \[
   d = 4v_c = 4 \times 80 = 320 \text{ km}
   \]

### Summary of Answers
a) The distance between Johor and Kuala Lumpur is 320 km.
b) The speed of the car is 80 km/h.

Would you like any further details or have any questions? 

Here are 5 additional questions you might consider:
1. How would the problem change if the car had to make a stop for 30 minutes during the journey?
2. What would be the speed of the bus?
3. How long would it take for the bus to reach Kuala Lumpur?
4. If the car increased its speed by 10 km/h, how much time would it save?
5. How much longer would the bus take to complete the journey compared to the car?

**Tip:** When dealing with problems involving relative speeds and distances, setting up equations systematically helps in solving them accurately.

Learn how to calculate the distance between Johor and Kuala Lumpur and determine the speed of a car using a problem-solving approach. This problem involves applying concepts of speed, distance, and time, and solving linear equations. Suitable for students in Grades 7-9.

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