Question

2
given a real - world model for a ratio of quantities with different units:
32
calculate a rate with or without a visual model (l3)
a car travels for 6 hours. using
the diagram below, how far did
the car travel after the first 4
hours?
number of hours
miles traveled
a painter uses several gallons of
paint for a new house. using the
diagram below, how many square
feet of wall can 3 gallons of paint
cover?
gallons of paint
square feet of wall

Explanation:

First Sub - Question (Car Travel Distance)

Step 1: Find the speed of the car

From the diagram, in 6 hours, the car travels 360 miles. The speed \(v\) is calculated by the formula \(v=\frac{\text{distance}}{\text{time}}\). So \(v = \frac{360}{6}=60\) miles per hour.

Step 2: Calculate distance for 4 hours

Using the formula \(\text{distance}=v\times t\), with \(v = 60\) mph and \(t = 4\) hours, we get \(\text{distance}=60\times4 = 240\) miles. We can also check from the diagram: at 3 hours, it's 180 miles (since \(60\times3 = 180\)), so at 4 hours, it should be \(60\times4=240\) miles.

Step 1: Find the coverage rate per gallon

From the diagram, 6 gallons cover 2269.5 square feet. The rate \(r\) is \(\frac{2269.5}{6}=378.25\) square feet per gallon. We can also check with 2 gallons: if 1 gallon is 378.25, 2 gallons should be \(378.25\times2 = 756.5\) square feet, which matches the diagram.

Step 2: Calculate coverage for 3 gallons

Using the formula \(\text{coverage}=r\times\text{gallons}\), with \(r = 378.25\) and gallons \(= 3\), we get \(\text{coverage}=378.25\times3=1134.75\) square feet.

Answer:

240 miles

Second Sub - Question (Paint Coverage)