Negative Rates and Distance Problems

This video tutorial covers the concept of negative rates, using examples like eating grapes, listening to songs, and running laps. It explores managing water levels in an aquarium with faulty systems, calculating the time for a submarine to reach Challenger Deep, and practical applications of rates in everyday scenarios. The video concludes with homework problems to reinforce the concepts.

What is the main focus of the lesson on negative rates?

• Understanding positive rates

• Applying knowledge of signed numbers to negative rates

• Learning about positive numbers

• Exploring positive rates in detail

If you eat 5 grapes per minute for 8 minutes, how many grapes will you eat in total?

• 40 grapes

• 30 grapes

• 50 grapes

• 60 grapes

How many songs can you listen to in 3 days if you listen to 9 new songs per day?

• 36 songs

• 27 songs

• 45 songs

• 18 songs

If a faucet fills an aquarium at 30 L per minute and a drain empties it at 20 L per minute, what is the net change in water level per minute?

• 10 L per minute decrease

• 10 L per minute increase

• 50 L per minute increase

• 50 L per minute decrease

How long will it take for the aquarium to overflow if it starts with 10,000 L and overflows at 12,000 L, given a net increase of 10 L per minute?

• 150 minutes

• 100 minutes

• 200 minutes

• 250 minutes

What is the depth of Challenger Deep below sea level?

• 30,000 ft

• 25,000 ft

• 40,000 ft

• 35,814 ft

Using the model y = -3x, how much time would it take to reach the bottom of Challenger Deep?

• 11,931 seconds

• 12,000 seconds

• 13,000 seconds

• 14,000 seconds

If a cookie recipe uses 3 cups of flour to make 15 cookies, how many cookies can be made with 4 cups of flour?

• 18 cookies

• 20 cookies

• 22 cookies

• 24 cookies

How much tape is needed to hang 10 student projects if 36 cm of tape is used for 9 projects?

• 44 cm

• 48 cm

• 52 cm

• 40 cm

What is the result of multiplying two negative numbers, such as -4 and -7?

• 14

• 28

• 0

• -28