Which distance and time combination results in a speed faster than 1 kilometer per hour?
2/5 km in 1/2 hour
3/4 km in 7/8 hour
2/3 km in 5/6 hour
1/3 km in 1/4 hour
To determine if the speed is faster than 1 kilometer per hour, we can convert the distance and time to kilometers and hours respectively.
1 kilometer = 1000 meters
1 hour = 60 minutes = 60 minutes/60 seconds = 1/60 hour
We can convert the given distance and time combinations to kilometers and hours as follows:
1) (2/5 km) * (1000 m/km) = (2/5) * (1000) = 400 meters
(1/2 hour) * (1/60 hour/minute) = (1/2) * (1/60) = 1/120 hour
2) (3/4 km) * (1000 m/km) = (3/4) * (1000) = 750 meters
(7/8 hour) * (1/60 hour/minute) = (7/8) * (1/60) = 7/480 hour
3) (2/3 km) * (1000 m/km) = (2/3) * (1000) = 666.67 meters (approximately)
(5/6 hour) * (1/60 hour/minute) = (5/6) * (1/60) = 5/360 hour
4) (1/3 km) * (1000 m/km) = (1/3) * (1000) = 333.33 meters (approximately)
(1/4 hour) * (1/60 hour/minute) = (1/4) * (1/60) = 1/240 hour
Now, we can calculate the speeds:
1) Speed = Distance / Time = 400 meters / (1/120 hour) = 400 * 120 = 48,000 meters/hour = 48 km/hour
The speed is faster than 1 kilometer per hour.
2) Speed = Distance / Time = 750 meters / (7/480 hour) = 750 * (480/7) = 51,428.57 meters/hour ≈ 51.43 km/hour
The speed is faster than 1 kilometer per hour.
3) Speed = Distance / Time = 666.67 meters / (5/360 hour) = 666.67 * (360/5) = 48,000 meters/hour = 48 km/hour
The speed is faster than 1 kilometer per hour.
4) Speed = Distance / Time = 333.33 meters / (1/240 hour) = 333.33 * (240/1) = 80,000 meters/hour = 80 km/hour
The speed is faster than 1 kilometer per hour.
Therefore, all four combinations of distances and times result in speeds faster than 1 kilometer per hour.
To determine which combination results in a speed faster than 1 kilometer per hour, we need to calculate the speed for each distance and time combination and compare them to 1 kilometer per hour (km/h).
1. Speed for the first combination (2/5 km in 1/2 hour):
Speed = Distance/Time
Speed = (2/5 km) / (1/2 hour)
Speed = (2/5) * (2/1)
Speed = 4/5 km/h
2. Speed for the second combination (3/4 km in 7/8 hour):
Speed = Distance/Time
Speed = (3/4 km) / (7/8 hour)
Speed = (3/4) * (8/7)
Speed = 6/7 km/h
3. Speed for the third combination (2/3 km in 5/6 hour):
Speed = Distance/Time
Speed = (2/3 km) / (5/6 hour)
Speed = (2/3) * (6/5)
Speed = 4/5 km/h
4. Speed for the fourth combination (1/3 km in 1/4 hour):
Speed = Distance/Time
Speed = (1/3 km) / (1/4 hour)
Speed = (1/3) * (4/1)
Speed = 4/3 km/h
Based on the calculations, none of the combinations have a speed faster than 1 kilometer per hour.