You pass a road sign saying "New York 112 km." If you drive at a constant speed of 65 mi / h, h

step 1 right. So you're driving. You're on the road, and you are 112 kilometers away from New York. You

You pass a road sign saying "New York 112 km." If you drive...

You pass a road sign saying "New York $112 \mathrm{~km}$." If you drive at a constant speed of $65 \mathrm{mi} / \mathrm{h}$, 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 $112 \mathrm{~km}$ ?

Key Concepts

Unit Conversion

This concept involves translating measurements from one unit system to another. In the context of the problem, distances are provided in kilometers while speeds are given in miles per hour, and fuel efficiency in miles per gallon must eventually be related to liters of gasoline. Mastering unit conversion is crucial for ensuring that calculations are consistent and that the results are expressed in the appropriate desired units.

Speed and Time Relationship

This concept describes the fundamental relationship between speed, distance, and time, usually expressed as time = distance ÷ speed. In this problem, understanding this relationship is essential for calculating how long it takes to travel a given distance at a constant speed, once the units are made consistent.

Fuel Efficiency Conversion

This involves converting a given fuel efficiency, expressed as miles per gallon, into an understanding of fuel usage over a specific distance in a different unit system (liters). This requires both converting the distance into compatible units and understanding the relationship between gallons and liters, which is critical for accurately determining the required amount of fuel.

Transcript

0:00 Right.

00:01 So you're driving.

00:01 You're on the road, and you are 112 kilometers away from new york.

00:06 You need to figure out how long that's gonna take you to get there.

00:09 If you are averaging 65 miles per hour ah, your car gets 28 miles to the gallon and you're gonna figure out have to figure out how much gas you're going to need.

00:20 Um, so these units, these unit conversions are these conversion factors i actually got from the first chapter of the textbook.

00:28 Um, so, um, the the examples in that first chapter between the text acts to a pretty good job walking you through how to convert from metric system units like kilometers and leaders to us system like miles and gallons.

00:45 So i would recommend taking a look at those at those examples.

00:48 Um, but i'm going to use those conversions.

00:51 So right, so the first thing we're gonna do is we're gonna have to figure out how many miles were traveling.

00:58 Um, so we're gonna convert the kilometers a mile is using the unit conversion here.

01:03 Right.

01:04 So it takes, um, 0.6 to 2 miles is one kilometer, right? so we're running about 69.

01:18 We're running.

01:18 We're driving about 69.664 miles and we're not gonna we're gonna go a few decimal places.

01:25 I think that the over answers are going to be rounded to two decimal points because of the 65 28 both have two significant figures.

01:34 I meant, say, significant figures, not decimal points.

01:37 Anyway, we're gonna multiply.

01:38 I said, now that we have our miles right, 69.664 miles, we're gonna use the mile per hour conversion factor to cancel out our miles, and we're gonna end up with ours.

01:50 So you have one alive.

01:52 Put it out there.

01:53 You're gonna put 69.664 miles, right? make sure that miles goes.

02:01 It's in the denominator, so you can set your miles out.

02:08 And when you do that and your rounds, you should get 1.1 hours...

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