Question

1. some boats were traveling up and down a river. a satellite recorded the movements of several boats.

a. a motor boat traveled -3.4 miles per hour for 0.75 hours. how far did it go?
b. a tugboat traveled -1.5 miles in 0.3 hours. what was its velocity?
c. what do you think that negative distances and velocities could mean in this situation?

1. from unit 5, lesson 11

evaluate each expression. when the answer is not a whole number, write your answer as a fraction.
a. $-4\cdot -6$
b. $-24\cdot \frac{-7}{6}$
c. $4\div -6$
d. $\frac{4}{3}\div -24$
5.
a. a cookie recipe uses 3 cups of flour to make 15 cookies. if you had 4 cups of flour, how many cookies could you make with this recipe? (assume you have enough of the other ingredients.)
b. 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?

Explanation:

Problem 3

Step1: Apply distance formula (d=v*t)

$d = -3.4 \times 0.75$

Step2: Calculate the product

$d = -2.55$

Step1: Apply velocity formula (v=d/t)

$v = \frac{-1.5}{0.3}$

Step2: Calculate the quotient

$v = -5$

Step1: Multiply two negative numbers

$-4 \times -6 = 24$

Step1: Simplify the multiplication

$-24 \times \frac{-7}{6} = \frac{24 \times 7}{6}$

Step2: Calculate the result

$\frac{168}{6} = 28$

Step1: Rewrite division as fraction

$4 \div -6 = -\frac{4}{6}$

Step2: Simplify the fraction

$-\frac{4}{6} = -\frac{2}{3}$

Step1: Rewrite division as multiplication

$\frac{4}{3} \div -24 = \frac{4}{3} \times \frac{1}{-24}$

Step2: Simplify the product

$\frac{4}{-72} = -\frac{1}{18}$

Step1: Find cookies per cup of flour

$\text{Cookies per cup} = \frac{15}{3} = 5$

Step2: Calculate cookies for 4 cups

$5 \times 4 = 20$

Step1: Find tape per project

$\text{Tape per project} = \frac{36}{9} = 4$

Step2: Calculate tape for 10 projects

$4 \times 10 = 40$

Answer:

a. -2.55 miles
b. -5 miles per hour
c. Negative distances and velocities mean the boats are traveling upstream (against the river's current), while positive values would represent traveling downstream (with the current).

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Problem 4