Four cities P, Q, R and S are on the corner of the square and the side of a square is 75 km. A businessman travels from P to Q at 5 km/h, Q to R at 3 km/h, R to S at 5 km/h and S to P at 3 km/h. Find his average speed of the whole journey.
To find the businessman's average speed for his entire journey, follow these steps:
The square has four cities on its corners: P, Q, R, and S. The side of the square is 75 km.
Calculate the total distance of the journey. Since the sides are of equal length, the total distance for the entire perimeter is:
\(4 \times 75 = 300 \, \text{km}\)
Determine the time taken for each leg of the journey:
- P to Q: Travels at 5 km/h thus taking: \(\frac{75}{5} = 15 \, \text{hours}\)
- Q to R: Travels at 3 km/h: \(\frac{75}{3} = 25 \, \text{hours}\)
- R to S: Travels again at 5 km/h: \(\frac{75}{5} = 15 \, \text{hours}\)
- S to P: Travels at 3 km/h: \(\frac{75}{3} = 25 \, \text{hours}\)
Calculate the total time taken for the entire journey: \(15 + 25 + 15 + 25 = 80 \, \text{hours}\)
Calculate the average speed. The total distance traveled is 300 km, and the total time taken is 80 hours. Thus, the average speed is:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{300}{80} = 3.75 \, \text{km/h}\)
Convert the average speed to a mixed fraction form: \(3.75 \, \text{km/h} = 3\frac{3}{4} \, \text{km/h}\)
Therefore, the average speed of the journey is \(3\frac{3}{4} \, \text{km/h}\), which corresponds to the option: $3\frac{3}{4}$ km/h.
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Important Questions from Average Speed
Kapil travels for 4.5 hours at a speed of 50 km / h and 7.5 hours at a speed of 70 km / h. At the end of it, he finds that he covered only 6/7 of the total distance. At what average speed should he travel so that the remaining distance traveled in 5 hours?
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A cylindrical road roller having a diameter of 1.5 m moves at a speed of 3km/h while levelling a road. How much length of the road will be levelled in 45 minutes?
