Question

Starting at home Michael travel uphill to the gift store for 24 minutes after 10 mph you can travel back home along the same path down hill at a speed of 30 mph what is his average speed for the entire trip from home to the gift store and back

Answer 1

The average speed for the entire trip from home to the gift store and back is 15 miles per hour

Solution:

Given that, Starting at home Michael travel uphill to the gift store for 24 minutes after 10 mph

1 hour = 60 minutes

$24\ minutes = \frac{24}{60}\ hour$

You can travel back home along the same path down hill at a speed of 30 mph

The distance is given as:

$distance = speed \times time$

Uphill distance:

$Uphill\ Distance = 10 \times \frac{24}{60} = 4 \text{ miles }$

The downhill distance will also be same 4 miles at a speed of 30 mph

Find the time taken for down trip

$time = \frac{4}{30} = 0.133$

Thus, time taken for downtrip = 0.133 hours

$Total\ time\ taken = \frac{24}{60} + 0.133\\\\Total\ time\ taken =0.533\ hours$

Total distance traveled = 4 miles + 4 miles = 8 miles

The average speed is given by formula:

$\text{Average Speed } = \frac{\text{Total distance traveled}}{\text{Total time taken}}$

Substituting the values we get,

$Average\ speed = \frac{8}{0.533} = 15.009 \approx 15$

Thus average speed for the entire trip from home to the gift store and back is 15 miles per hour