After repairing, a truck moves at a speed of 90 km/h, while before repairing it used to move at a speed of 80 km/h. After repairing, it covers a distance x in 8 hours. If the same truck were to cover four times that distance (4x) at its older speed before repairing, how much time (in hours) would it take?

Introduction / Context:
This question examines the relationship between distance, speed, and time when a vehicle has two different speeds before and after repair. It tests the ability to compute distance from speed and time, and then reuse this distance to find another time value at a different speed. The structure is straightforward but reinforces accurate use of basic formulas in time and distance problems.

Given Data / Assumptions:

Speed of the truck after repairing = 90 km/h.
Speed of the truck before repairing = 80 km/h.
After repair, the truck covers a distance x in 8 hours.
We need the time taken to cover 4x distance at the old speed of 80 km/h.
Speeds are constant during each scenario and there are no breaks.

Concept / Approach:
First, we compute the distance x using distance = speed * time for the truck after repairing. Then we multiply this distance by 4 to obtain 4x. Next, we calculate the time needed to cover 4x at the older speed before repairing using time = distance / speed. This two step approach shows how distance acts as a bridge between different speed and time combinations.

Step-by-Step Solution:
Step 1: Compute distance x covered after repairing. Speed = 90 km/h and time = 8 hours. Step 2: Distance x = 90 * 8 = 720 kilometres. Step 3: We are asked for the time taken to cover 4x at the old speed. So 4x = 4 * 720 = 2880 kilometres. Step 4: Before repairing, the speed was 80 km/h. Step 5: Time to cover 2880 kilometres at 80 km/h = distance / speed = 2880 / 80 hours. Step 6: Evaluate 2880 / 80 = 36 hours. Step 7: Therefore, the truck would take 36 hours to cover 4x distance at the older speed.

Verification / Alternative check:
We can reduce the fraction differently. Time = 4x / 80 = (4 * 720) / 80 hours. Simplify: 720 / 80 = 9. So time = 4 * 9 = 36 hours. This alternative calculation arrives at the same result, confirming the correctness of the answer.

Why Other Options Are Wrong:
If the time were 40 hours or 48 hours, the implied distances would be 40 * 80 = 3200 km or 48 * 80 = 3840 km, which are not equal to 2880 km. A value of 28 hours would give only 2240 km, and 32 hours would give 2560 km, both inconsistent with four times the original distance of 720 km. Only 36 hours is consistent with 4x = 2880 km at 80 km/h.

Common Pitfalls:
A common error is to forget to multiply the distance x by 4 before calculating the time, or to confuse which speed corresponds to which part of the journey. Another mistake is to miscalculate 90 * 8 or 2880 / 80. Keeping track of the two scenarios separately and writing down each step avoids these issues.

Final Answer:
The truck would take 36 hours to cover four times the original distance at its older speed of 80 km/h.