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.
Similar Questions
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- A salesman has to cover 6 km in $\frac{3}{4}$ h. If he covers $\frac{1}{2}$ of the distance in $\frac{2}{3}$ of the total time, then what must be his speed (in km/h) to cover the remaining distance in the remaining time?
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Important Questions from Speed Time and Distance
A journey of 900 km is completed in 11 h. If two-fifth of the journey is completed at the speed of 60 km/h, at what speed (in km/h) is the remaining journey completed?
A car starts from point A towards point B, travelling at the speed of 20 km/h. 1 \(\frac{1}{2}\) hours later, another car starts from point A and travelling at the speed of 30 km/h and reaches 2 \(\frac{1}{2}\) hours before the first car. Find the distance between A and B.
A bus covered a distance of 162 km. If speed of this bus is 15 m/s, then what will be the time taken ?
An athlete runs an 800 m race in 96 seconds. His speed (in km / h) is:
A person has to cover a distance of 150 km in 15 hours. If he traveled with the speed of 11.8 km/hr for 10 hours. At what speed he has to travel to cover the remaining distance in the remaining time?
