Answer :
Sure, let's break down the solution step-by-step:
1. Initial Journey Details:
The motorist originally takes 4.5 hours to reach his destination, traveling at a speed of 80 km/h.
2. Calculate the Distance:
To find out how far the motorist travels, we use the formula for distance:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
Substituting the known values:
[tex]\[
\text{Distance} = 80 \, \text{km/h} \times 4.5 \, \text{hours} = 360 \, \text{km}
\][/tex]
3. Speed for a 4-hour Journey:
If the motorist wants to complete the same 360 km journey in 4 hours, we find the needed speed by rearranging the distance formula to solve for speed:
[tex]\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\][/tex]
Thus:
[tex]\[
\text{Speed} = \frac{360 \, \text{km}}{4 \, \text{hours}} = 90 \, \text{km/h}
\][/tex]
So, he must travel at 90 km/h to complete the journey in 4 hours.
4. Time for a Speed of 110 km/h:
If he drives at 110 km/h, we find out how long it will take to cover the 360 km by using the formula for time:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\][/tex]
This gives:
[tex]\[
\text{Time} = \frac{360 \, \text{km}}{110 \, \text{km/h}} \approx 3.27 \, \text{hours}
\][/tex]
5. Converting Decimal Hours to Hours and Minutes:
We convert 3.27 hours into hours and minutes. The whole number part is already in hours, which is 3 hours.
For the minutes, take the fractional part (0.27) and multiply by 60 (since there are 60 minutes in an hour):
[tex]\[
0.27 \times 60 \approx 16 \, \text{minutes}
\][/tex]
Hence, at a speed of 110 km/h, the journey takes approximately 3 hours and 16 minutes.
That concludes the solution for the question!
1. Initial Journey Details:
The motorist originally takes 4.5 hours to reach his destination, traveling at a speed of 80 km/h.
2. Calculate the Distance:
To find out how far the motorist travels, we use the formula for distance:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
Substituting the known values:
[tex]\[
\text{Distance} = 80 \, \text{km/h} \times 4.5 \, \text{hours} = 360 \, \text{km}
\][/tex]
3. Speed for a 4-hour Journey:
If the motorist wants to complete the same 360 km journey in 4 hours, we find the needed speed by rearranging the distance formula to solve for speed:
[tex]\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\][/tex]
Thus:
[tex]\[
\text{Speed} = \frac{360 \, \text{km}}{4 \, \text{hours}} = 90 \, \text{km/h}
\][/tex]
So, he must travel at 90 km/h to complete the journey in 4 hours.
4. Time for a Speed of 110 km/h:
If he drives at 110 km/h, we find out how long it will take to cover the 360 km by using the formula for time:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\][/tex]
This gives:
[tex]\[
\text{Time} = \frac{360 \, \text{km}}{110 \, \text{km/h}} \approx 3.27 \, \text{hours}
\][/tex]
5. Converting Decimal Hours to Hours and Minutes:
We convert 3.27 hours into hours and minutes. The whole number part is already in hours, which is 3 hours.
For the minutes, take the fractional part (0.27) and multiply by 60 (since there are 60 minutes in an hour):
[tex]\[
0.27 \times 60 \approx 16 \, \text{minutes}
\][/tex]
Hence, at a speed of 110 km/h, the journey takes approximately 3 hours and 16 minutes.
That concludes the solution for the question!
