The mass of 42 identical books is 8,4kg.What is the mass of 12 of these books?
An aeroplane files 1400km in 1h 45mins. How far will it fly in 2h 30mins at the same average speed?
A road map is drawn to a scale of 1mm 50m. Calculate
The distance on the map which represent 20km on the road
The distance on the road which correspond to 228mm on the map
To find the mass of 12 of these books, we can use the concept of proportionality. Since the mass of 42 books is 8.4kg, we can express this as:
42 books / 8.4kg = 12 books / x
Cross-multiplying, we get:
42 books * x = 8.4kg * 12 books
Simplifying:
42x = 100.8kg
Dividing both sides by 42:
x = 2.4kg
Therefore, the mass of 12 of these books is 2.4kg.
To find how far the airplane will fly in 2 hours and 30 minutes, we can use the concept of average speed. The average speed is given as 1400km in 1 hour and 45 minutes, which is equal to 1.75 hours.
The distance traveled can be expressed as:
Distance = Average Speed * Time
Therefore,
Distance = 1400km * (2.5 hours)
Distance = 3500km
Therefore, the airplane will fly 3500km in 2 hours and 30 minutes at the same average speed.
For the road map scale, 1mm represents 50m on the actual road.
To calculate the distance on the map that represents 20km on the road, we can use the concept of proportionality:
1mm / 50m = x mm / 20km
Cross-multiplying, we get:
1mm * 20km = 50m * x mm
20km = 50m * x mm
Multiplying both sides by 1000 to convert km to mm:
20,000m = 50m * x mm
Dividing both sides by 50:
400mm = x mm
Therefore, the distance on the map that represents 20km on the road is 400mm.
To calculate the distance on the road that corresponds to 228mm on the map, we can again use proportionality:
1mm / 50m = 228mm / x km
Cross-multiplying, we get:
1mm * x km = 50m * 228mm
x km = 50m * 228mm
Dividing both sides by 1000 to convert mm to km:
x km = (50m * 228mm) / 1000
x km = 11.4km
Therefore, the distance on the road that corresponds to 228mm on the map is 11.4km.