Average Speed Calculation Steps
To determine the average speed for the entire journey, we need to calculate the total distance traveled and divide it by the total time spent traveling.
Part 1: Initial Driving Phase
- Speed (\(v_1\)): \(59\) kmph
- Time (\(t_1\)): \(3.5\) hours
- Distance covered (\(d_1\)): Calculated as Speed × Time. \( d_1 = v_1 \times t_1 \) \( d_1 = 59 \text{ kmph} \times 3.5 \text{ hours} = 206.5 \text{ km} \)
Part 2: Increased Speed Phase
- Speed increase: \(9\) kmph
- New Speed (\(v_2\)): The speed increased from the initial speed. \( v_2 = v_1 + 9 \text{ kmph} \) \( v_2 = 59 \text{ kmph} + 9 \text{ kmph} = 68 \text{ kmph} \)
- Time (\(t_2\)): \(1\) hour
- Distance covered (\(d_2\)): Calculated as New Speed × Time. \( d_2 = v_2 \times t_2 \) \( d_2 = 68 \text{ kmph} \times 1 \text{ hour} = 68 \text{ km} \)
Total Journey Summary
- Total Distance (\(D\)): Sum of distances from both parts. \( D = d_1 + d_2 \) \( D = 206.5 \text{ km} + 68 \text{ km} = 274.5 \text{ km} \)
- Total Time (\(T\)): Sum of times from both parts. \( T = t_1 + t_2 \) \( T = 3.5 \text{ hours} + 1 \text{ hour} = 4.5 \text{ hours} \)
Final Average Speed Calculation
The average speed (\(v_{avg}\)) is the total distance divided by the total time.
\( v_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{D}{T} \)
Substituting the calculated values:
\( v_{avg} = \frac{274.5 \text{ km}}{4.5 \text{ hours}} \)
\( v_{avg} = 61 \text{ kmph} \)
Similar Questions
A cyclist covers 120 meters in 16 seconds on a straight road, then immediately covers 180 meters in 24 seconds on a similar road segment. What is the average speed of the cyclist during the entire journey?
A runner completes one lap of a 200 meter circular track in 50 seconds. What is the average speed of the runner?
If a scooter travels at a constant speed of 25 km per hour, how far will it travel in 4 hours?
- Raj takes $2 \frac{1}{3}$ hours to complete a certain distance at a speed of 51 km/hr. What time would Kiran take to complete the same distance at a speed of 68km/hr?
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:
If Rohit can cover a distance of 1188 km in 22 hours, then what is the speed of Rohit?
A train is moving at 72 km/hrs. The distance covers in 15 minutes by the train is:
If Sonu is driving a car at a speed of 20 m/s, then in how much time Sonu will cover a distance of 936 km?
A person crosses a 1600 m long street in 4 min. What is his speed (in km/h)?
