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Chapter 1: Problem 56

You pass a road sign saying 鈥淣ew York 112 km.鈥� If you drive at a constant speed of 65 mi/h, how long should it take you to reach New York? If your car gets 28 miles to the gallon, how many liters of gasoline are necessary to travel 112 km?

Short Answer

Expert verified
It should take approximately 64.25 minutes to reach New York driving at a constant speed of 65 mi/h. Approximately 9.413 liters of gasoline are necessary to travel 112 km with a car that gets 28 miles to the gallon.

Step by step solution

01

Convert distance unit from kilometers to miles

To convert 112 km to miles, we can use the following unit conversion factor: 1 mile 鈮� 1.60934 km. Therefore, we can divide the given distance (112 km) by the conversion factor to obtain distance in miles. 112 km * (1 mile / 1.60934 km) = 69.594 mi
02

Convert speed unit from miles per hour to kilometers per hour

To convert 65 mi/h to km/h, we can multiply the given speed by the conversion factor: 1 mile 鈮� 1.60934 km. 65 mi/h * (1.60934 km / 1 mile) = 104.607 km/h
03

Calculate the time to reach New York

Now that we have converted the speed and distance to the same unit (km), we can calculate the time (in hours) to reach New York using the formula: time = distance 梅 speed time = 112 km 梅 104.607 km/h 鈮� 1.0708 h
04

Convert time to minutes

To convert the time required to reach New York from hours to minutes, multiply it by 60 (since there are 60 minutes in an hour). 1.0708 h * 60 minutes/h = 64.25 minutes
05

Calculate the fuel consumption in miles per gallon

We are given that the car gets 28 miles per gallon. To find out how many gallons of fuel are needed to cover the distance of 69.594 miles, divide the distance by the car's fuel consumption rate. gallons needed = 69.594 miles 梅 28 miles/gallon 鈮� 2.4855 gallons
06

Convert gallons to liters

To convert gallons to liters, we can use the following conversion factor: 1 gallon 鈮� 3.78541 liters. Therefore, we can multiply the gallons needed by the conversion factor to obtain liters of gasoline required. liters needed = 2.4855 gallons * (3.78541 liters / 1 gallon) 鈮� 9.413 liters It should take approximately 64.25 minutes to reach New York, and approximately 9.413 liters of gasoline are necessary to travel the 112 km distance.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distance Conversion
Distance conversion is a crucial part of solving problems that involve different measurement units. When you're dealing with distance conversion, you typically need a conversion factor, which is a number that relates two different units of measure. In this exercise, we are converting kilometers (km) to miles (mi).
To perform this conversion, we use the conversion factor: 1 mile is approximately 1.60934 kilometers. By knowing this, you can convert kilometers to miles by dividing the number of kilometers by 1.60934, like this:
  • 112 km 梅 1.60934 = 69.594 miles
This simple arithmetic gives us the distance in miles, allowing us to use the same units to perform subsequent calculations such as calculating travel time or fuel requirements.
Speed Conversion
Speed conversion is another common task that often goes hand-in-hand with distance conversion, especially when you're dealing with travel-related problems. Here, we convert speed from miles per hour (mi/h) to kilometers per hour (km/h).
To achieve this, you use the same conversion factor as with distance: 1 mile is approximately 1.60934 kilometers. Transforming speed to a different unit involves multiplying the speed in miles per hour by this factor:
  • 65 mi/h 脳 1.60934 = 104.607 km/h
By converting speed, it allows you to work within one unit system, making the process of finding time or fuel consumption more seamless.
Fuel Efficiency
Understanding fuel efficiency in terms of miles per gallon (mi/gal) versus liters per kilometer is essential, as fuel metrics often change depending on the region or country. In this exercise, the car's fuel efficiency is given as 28 miles per gallon.
First, calculate how many gallons are needed using the converted distance:
  • 69.594 miles 梅 28 miles/gallon = 2.4855 gallons
Then convert these gallons into liters using the conversion factor: 1 gallon is approximately 3.78541 liters:
  • 2.4855 gallons 脳 3.78541 = 9.413 liters
By understanding these conversions, you gain the flexibility to work with different units and comprehensively evaluate fuel needs for various distances.

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Most popular questions from this chapter

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