IM 7.5.12 Lesson: Negative Rates
If you eat 5 grapes per minute for 8 minutes, how many grapes will you eat?[br]
If you hear 9 new songs per day for 3 days, how many new songs will you hear?[br]
If you run 15 laps per practice, how many practices will it take you to run 30 laps?[br]
[size=150]A large aquarium should contain 10,000 liters of water when it is filled correctly. It will overflow if it gets up to 12,000 liters. The fish will get sick if it gets down to 4,000 liters. The aquarium has an automatic system to help keep the correct water level. If the water level is too low, a faucet fills it. If the water level is too high, a drain opens.[br][br]One day, the system stops working correctly. The faucet starts to fill the aquarium at a rate of 30 liters per minute, and the drain opens at the same time, draining the water at a rate of 20 liters per minute.[/size][br][br]Is the water level rising or falling? How do you know?
How long will it take until the tank starts overflowing or the fish get sick?[br]
[size=150]A different aquarium should contain 15,000 liters of water when filled correctly. It will overflow if it gets to 17,600 liters.[/size][br][br]One day there is an accident and the tank cracks in 4 places. Water flows out of each crack at a rate of [math]\frac{1}{2}[/math] liter per hour. An emergency pump can re-fill the tank at a rate of 2 liters per minute. How many minutes must the pump run to replace the water lost each hour?
Challenger Deep is the deepest known point in the ocean, at 35,814 feet below sea level. In 1960, Jacques Piccard and Don Walsh rode down in the Trieste and became the first people to visit the Challenger Deep.
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[/img][br]If sea level is represented by 0 feet, explain how you can represent the depth of a submarine descending from sea level to the bottom of Challenger Deep.[br]
Trieste’s descent was a change in depth of -3 feet per second. We can use the relationship [math]y=-3x[/math] to model this, where [math]y[/math] is the depth (in feet) and [math]x[/math] is the time (in seconds). Using this model, how much time would the Trieste take to reach the bottom?[br]
It took the Trieste 3 hours to ascend back to sea level. This can be modeled by a different relationship [math]y=kx[/math]. What is the value of [math]k[/math] in this situation?[br]
[size=150]The design of the Trieste was based on the design of a hot air balloon built by Auguste Piccard, Jacques's father. In 1932, Auguste rode in his hot-air balloon up to a record-breaking height.[/size][br][br]Auguste's ascent took 7 hours and went up 51,683 feet. Write a relationship [math]y=kx[/math] to represent his ascent from his starting location.[br]
Auguste's descent took 3 hours and went down 52,940 feet. Write another relationship to represent his descent.[br]
Did Auguste Piccard end up at a greater or lesser altitude than his starting point? How much higher or lower?[br]
During which part of either trip was a Piccard changing vertical position the fastest?
Explain why you chose the answer you did above.
IM 7.5.12 Practice: Negative Rates
Describe a situation where each of the following quantities might be useful.
[math]-20[/math] gallons per hour[br]
[math]-10[/math] feet per minute
[math]-0.1[/math] kilograms per second
A submarine is only allowed to change its depth by rising toward the surface in 60-meter stages. It starts off at -340 meters.
At what depth is it after 1 stage?
At what depth is it after 2 stages?
At what depth is it after 4 stages?
How many stages will it take to return to the surface?
Some boats were traveling up and down a river. A satellite recorded the movements of several boats.
A motor boat traveled -3.4 miles per hour for 0.75 hours. How far did it go?[br]
A tugboat traveled -1.5 miles in 0.3 hours. What was its velocity?[br]
What do you think that negative distances and velocities could mean in this situation?[br]
A cookie recipe uses 3 cups of flour to make 15 cookies. How many cookies can you make with this recipe with 4 cups of flour? (Assume you have enough of the other ingredients.)[br]
A teacher uses 36 centimeters of tape to hang up 9 student projects. At that rate, how much tape would the teacher need to hang up 10 student projects?[br]
Evaluate each expression. When the answer is not a whole number, write your answer as a fraction.
[math]-4\cdot-6[/math]
[math]-24\cdot-\frac{7}{6}[/math]
[math]4\div-6[/math]
[math]\frac{4}{3}\div-24[/math]