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 = (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 * time`

Uphill distance:

`Uphill\ Distance = 10 * (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 = (4)/(30) = 0.133`

Thus, time taken for downtrip = 0.133 hours

`Total\ time\ taken = (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 = (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