Calculating Distance Using Raj's Travel Details
First, we need to find the distance covered. We are given Raj's time and speed.
- Raj's time: $2 \frac{1}{3}$ hours. Convert this to an improper fraction: $2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}$ hours.
- Raj's speed: 51 km/hr.
- Use the formula: Distance = Speed $\times$ Time.
- Distance = $51 \text{ km/hr} \times \frac{7}{3} \text{ hours}$.
- Distance = $\frac{51 \times 7}{3} \text{ km} = 17 \times 7 \text{ km} = 119 \text{ km}$.
Finding Kiran's Time for the Same Distance
Now, we use the calculated distance and Kiran's speed to find the time Kiran would take.
- Distance: 119 km.
- Kiran's speed: 68 km/hr.
- Use the formula: Time = Distance / Speed.
- Kiran's Time = $\frac{119 \text{ km}}{68 \text{ km/hr}}$.
- Simplify the fraction: $\frac{119}{68} = \frac{17 \times 7}{17 \times 4} = \frac{7}{4}$ hours.
Converting Time to Mixed Fraction Format
Convert the improper fraction $\frac{7}{4}$ hours into a mixed number.
- $\frac{7}{4} \text{ hours} = 1 \frac{3}{4}$ hours.
Therefore, Kiran would take $1 \frac{3}{4}$ hours to complete the same distance.
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Important Questions from Speed Time and Distance
The average speed of a train is 180% of the average speed of a car. The car covers a distance of 990 km in 15 hours. The time taken (in hours) by the train to cover the distance of 891 km is:
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A person crosses a 1600 m long street in 4 min. What is his speed (in km/h)?
