1. If a map has a scale of 1cm to 30km, what distance would 1mm represent?
2. If it takes a spacecraft 3 days to travel 250,000 kilometres, what length of time will it take to travel one million kilometres?
3. A publican makes 75 cents on every bottle of beer she sells. How much profit will she make on 100 bottles?
1 mm is 1/10 of 1 cm.
1,000,000 km = 4 * 250,000
.75 * 100 = ?
1. To find the distance 1mm represents on the map, we need to multiply the scale by the length of 1mm.
First, let's convert the scale to the same units as the distance in question. Since the scale is in centimeters (cm) and the distance is in kilometers (km), we need to convert km to cm.
1 km = 100,000 cm (since 1 km equals 1000 meters and 1 meter equals 100 centimeters).
Now, we can proceed with the calculation.
1 cm represents 30 km (according to the given scale).
Therefore, 1 mm represents (1/10) cm or 0.1 cm.
To find the distance represented by 1 mm on the map:
0.1 cm represents (30 km / 1 cm) = 3 km.
Therefore, 1 mm on the map represents a distance of 3 kilometers.
2. To figure out the length of time it will take to travel one million kilometers, we can use the given information of the spacecraft's travel speed.
The spacecraft takes 3 days to travel 250,000 kilometers. To determine the time it will take to travel one million kilometers, we can set up a proportion:
(250,000 km)/(3 days) = (1,000,000 km)/(x days).
Cross-multiplying, we have:
(250,000 km) * (x days) = (1,000,000 km) * (3 days).
Simplifying the equation:
250,000x = 3,000,000.
Dividing both sides by 250,000:
x = 12.
Therefore, it will take the spacecraft 12 days to travel one million kilometers.
3. To calculate the profit made on 100 bottles of beer, we need to multiply the profit per bottle by the number of bottles.
The profit per bottle is 75 cents.
To find the profit on 100 bottles:
Profit = (Profit per bottle) * (Number of bottles)
Profit = 75 cents * 100 bottles
Profit = 7500 cents
Since 1 dollar equals 100 cents, we can convert the profit:
Profit = 7500 cents / 100 cents per dollar
Profit = $75.
Therefore, the publican will make a profit of $75 on 100 bottles of beer.
1. To determine the distance 1mm represents on a map with a scale of 1cm to 30km, we can set up a proportion:
1cm : 30km = 1mm : x
We can cross-multiply and solve for x:
1cm * x = 1mm * 30km
x = (1mm * 30km) / 1cm
By substituting the values and calculating, we find:
x = (1 * 30,000,000) / 10
x = 300,000 mm
Therefore, 1mm on the map represents a distance of 300,000 mm or 300 meters in real life.
2. To calculate the time it will take for the spacecraft to travel one million kilometers, we can set up a proportion based on the given information:
3 days : 250,000 km = x days : 1,000,000 km
Cross-multiplying and solving for x:
3 days * 1,000,000 km = 250,000 km * x days
3,000,000 days = 250,000 km * x
Dividing both sides by 250,000 km:
3,000,000 days / 250,000 km = x
x = 12 days
Therefore, it will take the spacecraft 12 days to travel one million kilometers.
3. To determine the profit made on 100 bottles of beer, we can multiply the price per bottle by the number of bottles:
Profit per bottle = 75 cents
Number of bottles = 100
Total profit = Profit per bottle * Number of bottles
Total profit = 75 cents * 100
Total profit = 7,500 cents or $75
Therefore, the publican will make a profit of $75 on 100 bottles of beer.