Average Speed Calculation for Ramesh's Journey

To determine the average speed, we need to find the total distance covered and divide it by the total time taken for the journey.

The formula for average speed is:

$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $

Calculating Total Distance

Ramesh's journey consists of two parts:

• Distance 1: 6 km
• Distance 2: 8 km

Total distance = 6 km + 8 km = 14 km.

Calculating Total Time

Time is calculated using the formula: $ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $

• Time for the first part (T₁): $ T_1 = \frac{6 \text{ km}}{5 \text{ km/h}} = 1.2 \text{ hours} $
• Time for the second part (T₂): $ T_2 = \frac{8 \text{ km}}{6 \text{ km/h}} = \frac{4}{3} \text{ hours} $

Total time = $ T_1 + T_2 = 1.2 \text{ h} + \frac{4}{3} \text{ h} $

To add these, we find a common denominator:

Total time = $ \frac{6}{5} \text{ h} + \frac{4}{3} \text{ h} = \frac{(6 \times 3) + (4 \times 5)}{15} \text{ h} = \frac{18 + 20}{15} \text{ h} = \frac{38}{15} \text{ hours} $

Calculating Average Speed

Using the total distance and total time:

$ \text{Average Speed} = \frac{14 \text{ km}}{\frac{38}{15} \text{ hours}} $

$ \text{Average Speed} = 14 \times \frac{15}{38} \text{ km/h} $

$ \text{Average Speed} = \frac{210}{38} \text{ km/h} $

Simplifying the fraction:

$ \text{Average Speed} = \frac{105}{19} \text{ km/h} $

Converting to a decimal:

$ \text{Average Speed} \approx 5.53 \text{ km/h} $

Thus, Ramesh's average speed is approximately 5.53 km/h.