Question

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?

Answer 1

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