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. Find the distance between Johor and Kuala Lumpur

Let \( d \) be the distance between Johor and Kuala Lumpur in kilometers.
Let \( v \) be the speed of the car in kilometers per hour.
Let \( v - 30 \) be the speed of the bus in kilometers per hour.

The car reached Kuala Lumpur in 4 hours, so:
\[
d = 4v
\]

The bus had traveled only \( \frac{5}{8} \) of the journey in 4 hours, so:
\[
\frac{5}{8}d = 4(v - 30)
\]

Substituting \( d = 4v \) into the bus's equation:
\[
\frac{5}{8}(4v) = 4(v - 30)
\]

Simplify:
\[
\frac{5}{2}v = 4v - 120
\]

Rearranging the terms:
\[
120 = 4v - \frac{5}{2}v
\]

Combine like terms:
\[
120 = \frac{8v - 5v}{2}
\]
\[
120 = \frac{3v}{2}
\]

Solve for \( v \):
\[
120 \times 2 = 3v
\]
\[
240 = 3v
\]
\[
v = 80
\]

Now, substitute \( v \) back to find \( d \):
\[
d = 4v = 4 \times 80 = 320 \, \text{km}
\]

Therefore, the distance between Johor and Kuala Lumpur is:
\[
\boxed{320 \, \text{km}}
\]

Would you like any additional details or have any questions?

Here are five more questions you can ask:

1. How do you calculate the speed of a vehicle given distance and time?
2. What is the formula for distance in terms of speed and time?
3. How can you solve problems involving proportional relationships in speed and distance?
4. What are some common units used for measuring speed, distance, and time?
5. How do you solve algebraic equations with fractions?

**Tip:** When dealing with word problems, always define your variables clearly and set up equations based on the relationships given in the problem. This helps to keep the solution organized and easier to follow.

Discover how to calculate the distance between Johor and Kuala Lumpur based on the speeds of a car and a bus. This problem illustrates key concepts in algebra and rate problems, providing a clear step-by-step solution. Distance calculated: 320 km.

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