To find the average speed for the entire journey, we need to calculate the total distance covered and the total time taken.
Calculating Time for Each Segment
The journey is divided into three equal segments of 160 km each.
- Segment 1: Distance = 160 km, Speed = 80 km/hr. Time taken (\(t_1\)) = \(\frac{\text{Distance}}{\text{Speed}} = \frac{160 \text{ km}}{80 \text{ km/hr}} = 2 \text{ hours}\).
- Segment 2: Distance = 160 km, Speed = 120 km/hr. Time taken (\(t_2\)) = \(\frac{\text{Distance}}{\text{Speed}} = \frac{160 \text{ km}}{120 \text{ km/hr}} = \frac{4}{3} \text{ hours}\).
- Segment 3: Distance = 160 km, Speed = 80 km/hr. Time taken (\(t_3\)) = \(\frac{\text{Distance}}{\text{Speed}} = \frac{160 \text{ km}}{80 \text{ km/hr}} = 2 \text{ hours}\).
Calculating Total Distance and Total Time
- Total Distance: The racer car covers 160 km in each of the three segments. Total Distance = \(160 \text{ km} + 160 \text{ km} + 160 \text{ km} = 480 \text{ km}\).
- Total Time: Sum the time taken for each segment. Total Time = \(t_1 + t_2 + t_3 = 2 \text{ hours} + \frac{4}{3} \text{ hours} + 2 \text{ hours}\). Total Time = \(4 + \frac{4}{3} = \frac{12}{3} + \frac{4}{3} = \frac{16}{3} \text{ hours}\).
Calculating Average Speed
The formula for average speed is Total Distance divided by Total Time.
Average Speed = \(\frac{\text{Total Distance}}{\text{Total Time}}\)
Average Speed = \(\frac{480 \text{ km}}{\frac{16}{3} \text{ hours}} = \frac{480 \times 3}{16} \text{ km/hr}\)
Average Speed = \(30 \times 3 \text{ km/hr} = 90 \text{ km/hr}\).
Therefore, the average speed of the racer car for the entire journey is 90 km/hr.
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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:
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)?
