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Problem:

A man covers a certain distance by his vehicle. If he moved 6 km/h faster, then he takes 4 hours less, and if he had moved 4 km/h slower, then he would have taken 4 hours more. Find his distance.

Let's define variables to solve the problem:

• Let the original speed of the man be $S$ km/h.
• Let the distance be $D$ km.
• The time taken to cover the distance at speed $S$ is $\frac{D}{S}$.

Given conditions:

1. If the speed is increased by 6 km/h, the time decreases by 4 hours: $\frac{D}{S + 6} = \frac{D}{S} - 4$

2. If the speed is decreased by 4 km/h, the time increases by 4 hours: $\frac{D}{S - 4} = \frac{D}{S} + 4$

Solving these two equations will give us the values of $D$ and $S$. I will now calculate the solution.

Let's proceed with solving the system of equations.The solution to the problem is:

• The man's original speed is $24$ km/h.
• The distance covered is $480$ km.

Would you like further details on the steps taken to solve this, or do you have any questions?

Here are 5 related questions for further practice:

1. What would happen if the man increased his speed by 10 km/h instead of 6 km/h?
2. If the man’s original speed was 30 km/h, how would the distance change under similar conditions?
3. How can we use a graph to represent the relationship between speed and time for this problem?
4. What happens to the time taken if both speed adjustments (increase and decrease) are the same value?
5. How would the equation change if instead of time changes, we were given different distances for the speed variations?

Tip: When solving word problems involving speed, distance, and time, carefully define variables and set up equations based on the relationships given in the problem.