Using Measurement to Solve Real-World Problems

Instructor: Gerald Lemay

Gerald has taught engineering, math and science and has a doctorate in electrical engineering.

This lesson uses fundamental and derived units with unit conversions to solve real-world problems like interpreting blueprints, counting the calories of a low-fat food, and estimating arrival time for high-speed driving.

Using Measurement to Solve Real-World Problems

Ever design a room makeover or look at plans for such a project?


Measuring on a blueprint
ruler_on_blueprints


This is a real-world problem. Solving these types of problems depends on measuring fundamental units (like distance, mass and time), deriving units (like distances per time), and performing unit conversions (like converting between km and miles). We will develop our measurement skills and problem solving abilities by:

  • Interpreting a blueprint
  • Estimating the calories in a low-fat meal
  • Calculating the arrival times associated with legal, high-speed driving

Blueprints

A blueprint is a scaled drawing of physical objects. A conference room might be 20 feet long and 14 feet wide. Scaling these fundamental units of distance using 1 foot is 1 inch gives a 20-inch by 14-inch rectangle. Twenty inches is a large dimension to draw on paper. Thus, a common scale for blueprints is 1/4 inch : 1 foot.

To draw this conference room with a 1/4 inch : 1 foot scale:

  • Divide the length, 20, by 4:

Blueprint dimension: 20 / 4 = 5 inches

  • Divide the width, 14, by 4:

Blueprint dimension: 14 / 4 = 3.5 inches

Measuring inches on the blueprint and converting to a dimension in feet, multiply by 4.

For example, the blueprint drawing for a conference room table measures 2 inches by 1 inch.

  • Actual dimension: 2 inches x 4 = 8 feet
  • Actual dimension: 1 inch x 4 = 4 feet

As a check, we visualize how nicely an 8-foot x 4-foot table fits into a 20-foot x 14-foot conference room.

To keep track of whether to divide or multiply by 4, use dimensional cancelling.


blueprint_to_actual


The ''inch'' unit cancels to leave ''feet.''

To scale actual dimensions to the blueprint drawing:


actual_to_blueprint


This time, the ''foot'' unit cancels.

Food Calories

Striving for a healthy weight, you buy 1% cottage cheese having 100 calories per serving size. One serving size is 1/2 cup (equivalent to 125 grams). The container has 500 grams.

Let's say your goal is 600 based on the derived unit of calories per meal. If you eat all the cottage cheese at one sitting, what part of your calorie quota have you used?

Solving this problem starts with asking how many 125-gram servings in the container? Right, 500/125 = 4. Note, ''gram'' is a fundamental unit of mass.

So, 4 times 100 calories is 400 calories. And 400/600 = 2/3 of the calorie quota for one meal.

We could also write:


food_calories


Of course, we get the same answer, but estimating is important before diving into formal expressions. Note, how all the units cancelled. Thus, we could just have easily arrived at 3/2 instead of 2/3 for a result. But an answer of 3/2 would say eating one container of the 1% cottage cheese is equivalent to 1.5 meals, which clearly is not the case! Overeating might really impact our measurement skills.

Autobahn Driving

The recommended speed limit on the Autobahn highway is 130 km/hour. If you could legally drive this fast to cover 120 miles, how long would it take?

Before writing an extensive expression involving the conversion of units, let's estimate the time.

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