Answer :
Certainly! Let's break down the problem step by step:
1. Initial Situation:
- The motorist takes 4.5 hours to complete his journey at a speed of 80 km/h.
- We need to find the total distance traveled to apply it in later calculations.
2. Calculate Total Distance:
- We know that distance can be calculated using the formula:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
- Here, the distance is:
[tex]\[
\text{Distance} = 80 \, \text{km/h} \times 4.5 \, \text{hours} = 360 \, \text{km}
\][/tex]
3. New Speed for 4-hour Journey:
- To find the speed needed to cover this distance in 4 hours, we use the formula:
[tex]\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\][/tex]
- So the new speed should be:
[tex]\[
\text{Speed} = \frac{360 \, \text{km}}{4 \, \text{hours}} = 90 \, \text{km/h}
\][/tex]
- Therefore, to complete the journey in 4 hours, the motorist must travel at 90 km/h.
4. Duration at 110 km/h:
- Now, if the motorist drives instead at 110 km/h, we need to find out how long the journey will take.
- Again, using the formula for time:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\][/tex]
- The time will be:
[tex]\[
\text{Time} = \frac{360 \, \text{km}}{110 \, \text{km/h}} \approx 3.27 \, \text{hours}
\][/tex]
- To convert 0.27 hours into minutes, we multiply by 60:
[tex]\[
0.27 \times 60 \approx 16.2 \, \text{minutes}
\][/tex]
- Thus, 0.27 hours is approximately 16 minutes.
5. Conclusion:
- At a speed of 110 km/h, the journey will take approximately 3 hours and 16 minutes.
In summary, the motorist must drive at 90 km/h to complete the journey in 4 hours. If he drives at 110 km/h, the journey will take about 3 hours and 16 minutes.
1. Initial Situation:
- The motorist takes 4.5 hours to complete his journey at a speed of 80 km/h.
- We need to find the total distance traveled to apply it in later calculations.
2. Calculate Total Distance:
- We know that distance can be calculated using the formula:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
- Here, the distance is:
[tex]\[
\text{Distance} = 80 \, \text{km/h} \times 4.5 \, \text{hours} = 360 \, \text{km}
\][/tex]
3. New Speed for 4-hour Journey:
- To find the speed needed to cover this distance in 4 hours, we use the formula:
[tex]\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\][/tex]
- So the new speed should be:
[tex]\[
\text{Speed} = \frac{360 \, \text{km}}{4 \, \text{hours}} = 90 \, \text{km/h}
\][/tex]
- Therefore, to complete the journey in 4 hours, the motorist must travel at 90 km/h.
4. Duration at 110 km/h:
- Now, if the motorist drives instead at 110 km/h, we need to find out how long the journey will take.
- Again, using the formula for time:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\][/tex]
- The time will be:
[tex]\[
\text{Time} = \frac{360 \, \text{km}}{110 \, \text{km/h}} \approx 3.27 \, \text{hours}
\][/tex]
- To convert 0.27 hours into minutes, we multiply by 60:
[tex]\[
0.27 \times 60 \approx 16.2 \, \text{minutes}
\][/tex]
- Thus, 0.27 hours is approximately 16 minutes.
5. Conclusion:
- At a speed of 110 km/h, the journey will take approximately 3 hours and 16 minutes.
In summary, the motorist must drive at 90 km/h to complete the journey in 4 hours. If he drives at 110 km/h, the journey will take about 3 hours and 16 minutes.
