Question

In the morning, David walked to school at a speed of 5km per hour. After walking for one third of an hour, he realized that he left his snacks, so he turned a ran at a speed of 8km per hour. After resting for 5 minutes he ran to school back again at the same speed. If it took 75 minutes, how many km is the home to the school?

Answer 1

The distance from David's home to school is 4.5 km.

Step-by-step explanation:

David's journey to school involves walking, running, and then running back. Let's break down the time and distances involved in each segment.

1. Walking to School:

David walks for one third of an hour at a speed of 5 km/h. The distance covered during this time is calculated as follows:

`\[ \text{Distance}_{\text{walk}} = \text{Speed}_{\text{walk}} * \text{Time}_{\text{walk}} = 5 \, \text{km/h} * (1)/(3) \, \text{h} = (5)/(3) \, \text{km}.\]`

2. *KRunning to Get Snacks and Back:

After realizing he forgot his snacks, David runs at a speed of 8 km/h. The total time spent running and resting is 75 minutes. Converting 5 minutes of resting to hours, we get
`\((5)/(60) \, \text{h}\)`. The distance covered while running is:

`\[ \text{Distance}_{\text{run}} = \text{Speed}_{\text{run}} * (\text{Time}_{\text{run}} + \text{Time}_{\text{rest}}) = 8 \, \text{km/h} * \left((5)/(60) \, \text{h} + (75)/(60) \, \text{h}\right) = (65)/(6) \, \text{km}.\]`

3. Running Back to School:

The remaining distance to school is covered at the same speed of 8 km/h. The distance is:

`\[ \text{Distance}_{\text{back}} = (5)/(3) \, \text{km}.\]`

Adding up all the distances, we get the total distance from home to school:

`\[ \text{Total Distance} = \text{Distance}_{\text{walk}} + \text{Distance}_{\text{run}} + \text{Distance}_{\text{back}} = (5)/(3) + (65)/(6) + (5)/(3) = 4.5 \, \text{km}.\]`

Therefore, the distance from David's home to school is 4.5 km.