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
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Important Questions from Speed Time and Distance
A train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is
Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.
Rohit and Dinesh are 64 km apart. Rohit can walk at a speed of 15 km/hr and Dinesh at the speed of 17 km/hr. In how many hours will they meet if they are travelling towards each other?
Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
A worker covers a distance of 81 km in 11 hours. He travels partly on foot at 4.5 km/h and partly on bicycle at 15 km/h. What is the distance covered on the cycle?
