Answer :
Sure! Let's find the average speed for each journey, step by step, rounded to the nearest whole number.
### a) 500 km in 6 hours and 10 minutes
1. Convert the time to hours:
- 10 minutes is equal to [tex]\( \frac{10}{60} \)[/tex] hours.
- Total time = [tex]\( 6 + \frac{10}{60} = 6.1667 \)[/tex] hours.
2. Calculate the average speed:
[tex]\[
\text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{500 \, \text{km}}{6.1667 \, \text{hours}} \approx 81 \, \text{km/h}
\][/tex]
### b) 64 km in 1 hour and 30 seconds
1. Convert the time to hours:
- 30 seconds is equal to [tex]\( \frac{30}{3600} \)[/tex] hours (since there are 3600 seconds in an hour).
- Total time = [tex]\( 1 + \frac{30}{3600} = 1.0083 \)[/tex] hours.
2. Calculate the average speed:
[tex]\[
\text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{64 \, \text{km}}{1.0083 \, \text{hours}} \approx 63 \, \text{km/h}
\][/tex]
### c) 36000 m in 45 minutes
1. Convert the distance to kilometers and the time to hours:
- Distance in kilometers = [tex]\( \frac{36000}{1000} = 36 \, \text{km} \)[/tex].
- 45 minutes is equal to [tex]\( \frac{45}{60} = 0.75 \)[/tex] hours.
2. Calculate the average speed:
[tex]\[
\text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{36 \, \text{km}}{0.75 \, \text{hours}} \approx 48 \, \text{km/h}
\][/tex]
### d) 320 m in 10 seconds
1. Convert the distance to kilometers and the time to hours:
- Distance in kilometers = [tex]\( \frac{320}{1000} = 0.32 \, \text{km} \)[/tex].
- 10 seconds is equal to [tex]\( \frac{10}{3600} \)[/tex] hours.
2. Calculate the average speed:
[tex]\[
\text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{0.32 \, \text{km}}{\frac{10}{3600} \, \text{hours}} \approx 115 \, \text{km/h}
\][/tex]
In summary, the average speeds are:
- Journey a: 81 km/h
- Journey b: 63 km/h
- Journey c: 48 km/h
- Journey d: 115 km/h
### a) 500 km in 6 hours and 10 minutes
1. Convert the time to hours:
- 10 minutes is equal to [tex]\( \frac{10}{60} \)[/tex] hours.
- Total time = [tex]\( 6 + \frac{10}{60} = 6.1667 \)[/tex] hours.
2. Calculate the average speed:
[tex]\[
\text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{500 \, \text{km}}{6.1667 \, \text{hours}} \approx 81 \, \text{km/h}
\][/tex]
### b) 64 km in 1 hour and 30 seconds
1. Convert the time to hours:
- 30 seconds is equal to [tex]\( \frac{30}{3600} \)[/tex] hours (since there are 3600 seconds in an hour).
- Total time = [tex]\( 1 + \frac{30}{3600} = 1.0083 \)[/tex] hours.
2. Calculate the average speed:
[tex]\[
\text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{64 \, \text{km}}{1.0083 \, \text{hours}} \approx 63 \, \text{km/h}
\][/tex]
### c) 36000 m in 45 minutes
1. Convert the distance to kilometers and the time to hours:
- Distance in kilometers = [tex]\( \frac{36000}{1000} = 36 \, \text{km} \)[/tex].
- 45 minutes is equal to [tex]\( \frac{45}{60} = 0.75 \)[/tex] hours.
2. Calculate the average speed:
[tex]\[
\text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{36 \, \text{km}}{0.75 \, \text{hours}} \approx 48 \, \text{km/h}
\][/tex]
### d) 320 m in 10 seconds
1. Convert the distance to kilometers and the time to hours:
- Distance in kilometers = [tex]\( \frac{320}{1000} = 0.32 \, \text{km} \)[/tex].
- 10 seconds is equal to [tex]\( \frac{10}{3600} \)[/tex] hours.
2. Calculate the average speed:
[tex]\[
\text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{0.32 \, \text{km}}{\frac{10}{3600} \, \text{hours}} \approx 115 \, \text{km/h}
\][/tex]
In summary, the average speeds are:
- Journey a: 81 km/h
- Journey b: 63 km/h
- Journey c: 48 km/h
- Journey d: 115 km/h
