When are They the Same?

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Compare Rates of Water Flow in Two Containers.

The amount of water in two tanks every 5 minutes is shown in the table.

(1). Describe what is happening in each tank. Either draw a picture in the applet below, say it verbally, or write a few sentences.

(2). Use the table to estimate when the tanks will have the same amount of water.

(3). The amount of water (in liters) in tank 1 after minutes is 30+ 25. The amount of water (in liters) in tank 2 after minutes is -20+ 1000. Find the time when the amount of water will be equal.

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Caculate the Height of an Elevator.

A building has two elevators that both go above and below ground.

At a certain time of day, the travel time it takes elevator A to reach height h in meters is 0.8h + 16 seconds.

The travel time it takes elevator B to reach height h in meters is – 0.8h + 16 seconds.

(1). What is the height of each elevator at this time?
(2). How long would it take each elevator to reach ground level at this time?
(3). If the two elevators travel toward one another, at what height do they pass each other?
(4). How long would it take?
(5). If you are on an underground parking level 14 meters below ground, which elevator would reach you first?

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Complete an Equation for a Missing Value.

(A). Enter the value of a below to complete each equation so that it is true for all values of.

(B). Find a value of b below to complete each equation so that it is true for no values of.

Describe how you know whether an equation will be true for all values of or true for no values of .

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Which story matches the equation -6 + 3 = 2 + 4?

A. At 5 p.m., the temperatures recorded at two weather stations in Antarctica are -6 degrees and 2 degrees. The temperature changes at the same constant rate, x degrees per hour, throughout the night at both locations. The temperature at the first station 3 hours after this recording is the same as the temperature at the second station 4 hours after this recording.

B. Elena and Kiran play a card game. Every time they collect a pair of matching cards, they earn x points. At one point in the game, Kiran has -6 points and Elena has 2 points. After Elena collects 3 pairs and Kiran collects 4 pairs, they have the same number of points.

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For what value of do the expressions and have the same value?

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Decide whether each equation is true for all, one, or no values of .