A bus is travelling with $\frac{7}{8}$ of its actual speed to cover 42 km in 1 h 16 min. Find the actual speed of the bus.
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.
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