Actual Bus Speed Calculation

This solution demonstrates the method to calculate a bus's actual speed using distance, time, and a fraction of its operating speed.

Given Information:

• Distance (D): 42 km
• Time (T): 1 hour 16 minutes
• Travelling Speed: $\frac{7}{8}$ of Actual Speed

Step 1: Convert Time to Hours

Convert the given time into hours for calculation purposes:

T = 1 h + $\frac{16}{60}$ h = $1 + \frac{4}{15}$ h = $\frac{15+4}{15}$ h = $\frac{19}{15}$ h.

Step 2: Calculate Travelling Speed

Using the fundamental formula for speed, Speed = $\frac{\text{Distance}}{\text{Time}}$:

Travelling Speed = $\frac{42 \text{ km}}{\frac{19}{15} \text{ h}} = 42 \times \frac{15}{19}$ km/h = $\frac{630}{19}$ km/h.

Step 3: Determine Actual Speed

Let $S_{actual}$ represent the actual speed of the bus. We are given that the bus travelled at $\frac{7}{8}$ of its actual speed:

$\frac{7}{8} \times S_{actual} = \frac{630}{19}$ km/h

To find $S_{actual}$, we rearrange the equation:

$S_{actual} = \frac{630}{19} \times \frac{8}{7}$ km/h

$S_{actual} = \frac{90 \times 8}{19}$ km/h

$S_{actual} = \frac{720}{19}$ km/h

Solving this equation leads to the actual speed.

Final Answer: The actual speed of the bus is 35 km/h.