Speed, Distance, and Time Calculation

This problem involves calculating the original speed given changes in speed and distance traveled over the same time period.

Problem Setup

• Let the original speed be $S$ km/h.
• The time taken for the journey is $T = 30$ hours.
• Let the total distance from Delhi to Kanyakumari be $D$ km.

Original Journey

Using the formula Distance = Speed × Time:

$D = S \times T$

$D = S \times 30$ (Equation 1)

Modified Journey

The speed is reduced by $\frac{1}{15}$th. The new speed is:

New Speed $= S - \frac{1}{15}S = \frac{15S - S}{15} = \frac{14}{15}S$ km/h.

In this modified journey, the distance covered is 10 km less than the original distance.

New Distance $= D - 10$ km.

The time taken remains the same: $T = 30$ hours.

Calculating the Speed

Using the formula Distance = Speed × Time for the modified journey:

New Distance $= \text{New Speed} \times T$

$D - 10 = (\frac{14}{15}S) \times 30$

$D - 10 = 14S \times 2$

$D - 10 = 28S$ (Equation 2)

Solving the Equations

Now, substitute the value of $D$ from Equation 1 into Equation 2:

$30S - 10 = 28S$

Rearrange the terms to solve for $S$:

$30S - 28S = 10$

$2S = 10$

$S = \frac{10}{2}$

$S = 5$ km/h

Conclusion

The original speed is 5 km/h.