Calculate the Exact Speed After the Truck's 7th Hour in a 15-Hour Journey

A truck travels for 4 hours at a speed of 30 km/h, then for 3 hours at a speed of 50 km/h.

If its average speed during 15 hours is 5X km/h, then what is its speed after the first 7 hours of travel?

To solve this problem, we'll follow these steps:

• Step 1: Calculate the distance traveled in the first 7 hours: 4 hours at 30 km/h, then 3 hours at 50 km/h.
• Step 2: Calculate the total distance over 15 hours using the average speed given as $5X$.
• Step 3: Use this total distance to find the speed after the first 7 hours.

Now, let's work through these steps:

Step 1: Calculate the distance in the first 4 hours traveling at 30 km/h.
The distance is $30 \text{ km/h} \times 4 \text{ hours} = 120 \text{ km}$.

Next, calculate the distance in the next 3 hours traveling at 50 km/h.
The distance is $50 \text{ km/h} \times 3 \text{ hours} = 150 \text{ km}$.

Total distance covered in the first 7 hours is $120 \text{ km} + 150 \text{ km} = 270 \text{ km}$.

Step 2: Calculate total distance over 15 hours using the average speed.
The average speed is given as $5X \text{ km/h}$, thus:
$\text{Total Distance} = \text{Average Speed} \times \text{Time} = (5X) \times 15 = 75X \text{ km}$.

Step 3: Determine the distance covered in the remaining 8 hours.
$\text{Remaining Distance} = 75X - 270 \text{ km}$.

Since this remaining distance is covered in 8 hours, the speed after the first 7 hours of travel is:
$\text{Speed} = \frac{75X - 270}{8}$.

Calculating this gives:
$\text{Speed} = 9.375X - 33.75$ km/h.

Therefore, the speed after the first 7 hours of travel is $9.375X - 33.75$ km/h.