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Contact [7]
3 years ago
15

You hike two thirds of the way to the top of a hill at a speed of 2.9 mi/h and run the final third at a speed of 5.6 mi/h. What

was your average speed?
Physics
1 answer:
Marta_Voda [28]3 years ago
3 0

Answer:

The average speed is 3.5 mi/h

Explanation:

Average speed is given by

Average speed = \frac{Total distance}{Total time}

If the total distance covered is x mi,

Then \frac{2}{3}x mi was covered while hiking and

\frac{1}{3}x mi was covered while running.

Now, we will find the time taken while hiking and the time taken while running

Speed = \frac{Distance}{ Time}\\  Time = \frac{Distance}{Speed}

  • For the time taken while hiking

Speed = 2.9 mi/h

Distance = \frac{2}{3}x mi

From,

Time = \frac{Distance}{Speed}

Time = \frac{\frac{2}{3}x }{2.9}

Time = 0.2299x h

Time taken while hiking is 0.2299 h

  • For the time taken while running

Speed = 5.6 mi/h

Distance = \frac{1}{3}x mi

Time = \frac{Distance}{Speed}

Time = \frac{\frac{1}{3}x }{5.6}

Time = 0.05952x h

Now, for the average speed

Average speed = \frac{Total distance}{Total time}

Total distance = \frac{2}{3}x mi  + \frac{1}{3}x mi = x mi

Total time = 0.2299x + 0.05952x = 0.28942x h

∴ Average speed = \frac{x}{0.28942x}

Average speed = 3.4552 mi/h

Average speed ≅ 3.5 mi/h

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