1) In Europe, gasoline efficiency is measured in km/L. If your car's gas mileage is 21.0 mi/gal , how many liters of gasoline would you need to buy to complete a 142-km trip in Europe? Use the following conversions: 1km=0.6214mi and 1gal=3.78L.
Answer "15.9" L
2) While in Europe, if you drive 101 km per day, how much money would you spend on gas in one week if gas costs 1.10 euros per liter and your car's gas mileage is 42.0 mi/gal ? Assume that 1euro=1.26 dollars.
_____ dollars
3) A sprinter set a high school record in track and field, running 200.0 m in 20.8 s . What is the average speed of the sprinter in kilometers per hour?
_____ km/h
4) A specific brand of gourmet chocolate candy contains 7.00 g of dietary fat in each 22.7-g piece. How many kilograms of dietary fat are in a box containing 4.00 lb of candy?
_____ kg
Katie, you need to tell us what you think with these problems. It helps if we know exactly what you don't understand about each problem. We don't want to do all of the thinking for you.
To do #1 you want to convert mi/gal to km/L. Use the conversion factors so that the units cancel. You can't go wrong that way.
21.0 mi/gal x (1 km/0.6214 mi) x (1 gal/3.78L) = ? km/L
Then ? km/L x how many L = 142 km. Solve for how many L.
1) To convert gasoline efficiency from miles per gallon (mi/gal) to kilometers per liter (km/L), we need to use the given conversions:
1 km = 0.6214 mi
1 gal = 3.78 L
First, let's convert the gas mileage from mi/gal to km/L.
Gas mileage = 21.0 mi/gal
To convert miles to kilometers, we multiply by the conversion factor:
21.0 mi * 1.60934 km/mi = 33.79674 km
To convert gallons to liters, we multiply by the conversion factor:
33.79674 km * (1 gal / 3.78 L) = 8.94429 L
Therefore, a car with a gas mileage of 21.0 mi/gal would need to buy 8.94429 liters of gasoline to complete a 142-km trip in Europe.
Answer: 8.94429 L
2) To calculate the amount of money spent on gas in one week, we need to first find out the total distance traveled in one week.
Distance per day = 101 km/day
Total distance per week = 101 km/day * 7 days = 707 km/week
To convert the gas mileage from mi/gal to km/L, we use the given conversion:
42.0 mi/gal
To convert miles to kilometers, we multiply by the conversion factor:
42.0 mi * 1.60934 km/mi = 67.59228 km
To convert gallons to liters, we multiply by the conversion factor:
67.59228 km * (1 gal / 3.78 L) = 17.86921 L
Now, we can calculate the amount of money spent on gas in one week.
Amount spent on gas = 17.86921 L * 1.10 euros/L
Since 1 euro = 1.26 dollars, we can convert the amount to dollars:
Amount spent on gas = 17.86921 L * 1.10 euros/L * 1.26 dollars/euro
Therefore, the amount spent on gas in one week would be 17.86921 L * 1.10 euros/L * 1.26 dollars/euro.
Answer: _____ dollars
3) To calculate the average speed, we need to use the formula:
Average speed = Total distance / Total time
Total distance = 200.0 m
Total time = 20.8 s
To convert meters to kilometers, we divide by 1000:
200.0 m / 1000 = 0.2 km
To convert seconds to hours, we divide by 3600:
20.8 s / 3600 = 0.00578 hours
Now we can calculate the average speed:
Average speed = 0.2 km / 0.00578 hours
Therefore, the average speed of the sprinter is _____ km/h.
4) To find the amount of dietary fat in a box containing 4.00 lb of candy, we need to first convert the weight of the candy to grams.
Weight of candy = 4.00 lb
To convert pounds to grams, we multiply by the conversion factor:
4.00 lb * 453.592 g/lb = 1814.368 g
Now we can calculate the amount of dietary fat in the candy box.
Amount of dietary fat = (7.00 g of fat / 22.7 g of candy) * 1814.368 g
Now we can convert grams to kilograms:
Amount of dietary fat = [(7.00 g of fat / 22.7 g of candy) * 1814.368 g] / 1000
Therefore, the amount of dietary fat in a box containing 4.00 lb of candy is _____ kg.
1) To convert the gasoline efficiency from miles per gallon (mi/gal) to kilometers per liter (km/L), you can use the following conversion factors:
1 km = 0.6214 mi
1 gal = 3.78 L
First, convert the car's gas mileage from mi/gal to km/L:
Gas mileage = 21.0 mi/gal
Gas mileage in km/L = (21.0 mi/gal) * (0.6214 km/mi) * (1 gal/3.78 L)
Gas mileage in km/L = 8.86 km/L
Now, to calculate how many liters of gasoline you would need to buy to complete a 142-km trip in Europe, you can use the formula:
Liters of gasoline = (Distance in km) / (Gas mileage in km/L)
Liters of gasoline = 142 km / 8.86 km/L
Liters of gasoline ≈ 16.04 L
Rounding to one decimal place, the answer is approximately 15.9 L.
2) To calculate how much money you would spend on gas in one week, you need to know the daily distance driven and the cost of gas per liter.
Given:
Distance driven per day = 101 km
Cost of gas = 1.10 euros per liter
Conversion rate: 1 euro = 1.26 dollars
First, convert the distance driven per day from km to miles:
Distance driven per day = 101 km * 0.6214 mi/km
Distance driven per day ≈ 62.82 mi
Next, convert the gas mileage from miles per gallon to liters per 100 km, as it is commonly used in Europe:
Gas mileage = 42.0 mi/gal
Gas mileage ≈ 42.0 mi/gal * (1.609 km/mi) / (3.785 L/gal) * (100 km/1,000 m)
Gas mileage ≈ 17.81 L/100 km
Now, calculate the liters of gasoline used per day:
Liters of gasoline per day = (Distance driven per day) / (Gas mileage in km/L)
Liters of gasoline per day ≈ 62.82 mi / [(17.81 L/100 km) * 100 km]
Liters of gasoline per day ≈ 62.82 mi / 17.81 L
Liters of gasoline per day ≈ 3.52 L
Next, calculate the cost of gas per day:
Cost of gas per day = (Liters of gasoline per day) * (Cost of gas per liter)
Cost of gas per day = 3.52 L * 1.10 euros/L
Cost of gas per day ≈ 3.87 euros
Finally, calculate the cost of gas per week by multiplying the cost of gas per day by 7:
Cost of gas per week = (Cost of gas per day) * 7
Cost of gas per week ≈ 3.87 euros * 7
Cost of gas per week ≈ 27.09 euros
To convert the cost of gas from euros to dollars, use the conversion rate:
Cost of gas per week in dollars = (Cost of gas per week) * (1 euro / 1.26 dollars)
Cost of gas per week in dollars ≈ 27.09 euros * (1 / 1.26) dollars/euro
Cost of gas per week in dollars ≈ 21.50 dollars
Therefore, the answer is approximately 21.50 dollars.
3) To calculate the average speed of the sprinter in kilometers per hour, you need to convert the distance and time given into the appropriate units.
Given:
Distance = 200.0 m
Time = 20.8 s
First, convert the distance from meters to kilometers:
Distance = 200.0 m * (1 km / 1,000 m)
Distance = 0.200 km
Next, convert the time from seconds to hours:
Time = 20.8 s * (1 min / 60 s) * (1 hour / 60 min)
Time ≈ 0.0058 hours (rounded to four decimal places)
Now, calculate the average speed using the formula:
Average speed = (Distance) / (Time)
Average speed = 0.200 km / 0.0058 hours
Average speed ≈ 34.48 km/h
Therefore, the average speed of the sprinter is approximately 34.48 km/h.
4) To calculate the amount of dietary fat in kilograms, you need to convert the given information and apply the appropriate conversion factors.
Given:
Dietary fat per piece = 7.00 g
Weight of candy = 4.00 lb
First, convert the weight of candy from pounds to grams:
Weight of candy = 4.00 lb * (453.59 g / 1 lb)
Weight of candy ≈ 1,814.36 g
Now, calculate the amount of dietary fat in kilograms using the formula:
Amount of dietary fat = (Dietary fat per piece / Weight of candy) * 1,000 g/kg
Amount of dietary fat = (7.00 g / 22.7 g) * 1,814.36 g/kg
Amount of dietary fat ≈ 5.542 kg
Therefore, the amount of dietary fat in the box of candy is approximately 5.542 kg.