Answer :
Certainly! Let's break this down step-by-step for each part of the question:
### Part a:
Question: A car drives 195 miles in 3 hours and 15 minutes. What is the average speed of the car?
1. Convert time to hours:
- We have 3 hours and 15 minutes.
- Since 15 minutes is \( \frac{15}{60} \) hours, we convert it to hours:
[tex]\[ \text{Time in hours} = 3 + \frac{15}{60} = 3 + 0.25 = 3.25 \, \text{hours} \][/tex]
2. Use the formula for average speed:
- Average speed is given by the distance divided by time:
[tex]\[ \text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{195 \, \text{miles}}{3.25 \, \text{hours}} \][/tex]
3. Calculate the average speed:
- The average speed is:
[tex]\[ \frac{195}{3.25} = 60 \, \text{miles per hour} \][/tex]
- Therefore, the average speed of the car is 60 miles per hour.
### Part b:
Question: A car drives at a speed of 90 km/h for 2 hours and 20 minutes. How far does the car drive?
1. Convert time to hours:
- We have 2 hours and 20 minutes.
- Since 20 minutes is \( \frac{20}{60} \) hours, we convert it to hours:
[tex]\[ \text{Time in hours} = 2 + \frac{20}{60} = 2 + \frac{1}{3} = 2 + 0.333 \approx 2.333 \, \text{hours} \][/tex]
2. Use the formula for distance:
- Distance is given by the speed multiplied by time:
[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} = 90 \, \text{km/h} \times 2.333 \, \text{hours} \][/tex]
3. Calculate the distance:
- The distance is:
[tex]\[ 90 \times 2.333 = 210 \, \text{km} \][/tex]
- Therefore, the car drives 210 kilometers.
### Part c:
Question: A bus drives 66 km at an average speed of 24 km/h. How long does the journey take?
1. Use the formula for time:
- Time is given by the distance divided by speed:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{66 \, \text{km}}{24 \, \text{km/h}} \][/tex]
2. Calculate the time:
- The time is:
[tex]\[ \frac{66}{24} = 2.75 \, \text{hours} \][/tex]
3. Convert to hours and minutes:
- \( 2.75 \) hours is equal to \( 2 \) hours and \( 0.75 \times 60 \) minutes:
[tex]\[ 0.75 \times 60 = 45 \, \text{minutes} \][/tex]
- Therefore, the journey takes 2 hours and 45 minutes.
Summarizing:
- a) The average speed of the car is 60 miles per hour.
- b) The car drives 210 kilometers.
- c) The bus journey takes 2 hours and 45 minutes.
### Part a:
Question: A car drives 195 miles in 3 hours and 15 minutes. What is the average speed of the car?
1. Convert time to hours:
- We have 3 hours and 15 minutes.
- Since 15 minutes is \( \frac{15}{60} \) hours, we convert it to hours:
[tex]\[ \text{Time in hours} = 3 + \frac{15}{60} = 3 + 0.25 = 3.25 \, \text{hours} \][/tex]
2. Use the formula for average speed:
- Average speed is given by the distance divided by time:
[tex]\[ \text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{195 \, \text{miles}}{3.25 \, \text{hours}} \][/tex]
3. Calculate the average speed:
- The average speed is:
[tex]\[ \frac{195}{3.25} = 60 \, \text{miles per hour} \][/tex]
- Therefore, the average speed of the car is 60 miles per hour.
### Part b:
Question: A car drives at a speed of 90 km/h for 2 hours and 20 minutes. How far does the car drive?
1. Convert time to hours:
- We have 2 hours and 20 minutes.
- Since 20 minutes is \( \frac{20}{60} \) hours, we convert it to hours:
[tex]\[ \text{Time in hours} = 2 + \frac{20}{60} = 2 + \frac{1}{3} = 2 + 0.333 \approx 2.333 \, \text{hours} \][/tex]
2. Use the formula for distance:
- Distance is given by the speed multiplied by time:
[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} = 90 \, \text{km/h} \times 2.333 \, \text{hours} \][/tex]
3. Calculate the distance:
- The distance is:
[tex]\[ 90 \times 2.333 = 210 \, \text{km} \][/tex]
- Therefore, the car drives 210 kilometers.
### Part c:
Question: A bus drives 66 km at an average speed of 24 km/h. How long does the journey take?
1. Use the formula for time:
- Time is given by the distance divided by speed:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{66 \, \text{km}}{24 \, \text{km/h}} \][/tex]
2. Calculate the time:
- The time is:
[tex]\[ \frac{66}{24} = 2.75 \, \text{hours} \][/tex]
3. Convert to hours and minutes:
- \( 2.75 \) hours is equal to \( 2 \) hours and \( 0.75 \times 60 \) minutes:
[tex]\[ 0.75 \times 60 = 45 \, \text{minutes} \][/tex]
- Therefore, the journey takes 2 hours and 45 minutes.
Summarizing:
- a) The average speed of the car is 60 miles per hour.
- b) The car drives 210 kilometers.
- c) The bus journey takes 2 hours and 45 minutes.
