On a recent trip, Lamar's distance varied directly with the number of hours he drove. He traveled 288 miles in 6 hours. Which equation shows Lamar's distance, d, based on the number of hours, h, he drove?
CLEAR SUBMIT
𝑑=6ℎ
d
=
6
h
𝑑=48ℎ
d
=
48
h
𝑑=50ℎ
d
=
50
h
𝑑=288ℎ
d = 288h
The correct equation that shows Lamar's distance, d, based on the number of hours, h, he drove is:
d = 48h
To solve this problem, we can use the concept of direct variation. In direct variation, two variables are proportional to each other, meaning that as one variable increases, the other also increases by a consistent ratio.
In this case, Lamar's distance (d) is directly proportional to the number of hours he drove (h). We can represent this relationship using the equation:
𝑑 = 𝑘ℎ
Where 𝑑 is the distance, 𝑘 is the constant of variation, and ℎ is the number of hours he drove.
To find the value of 𝑘, we can use the given information that Lamar traveled 288 miles in 6 hours. Substituting these values into the equation, we get:
288 = 𝑘 * 6
Simplifying the equation:
𝑘 = 48
Now that we know the value of 𝑘, we can substitute it back into the original equation to express Lamar's distance based on the number of hours:
𝑑 = 48ℎ
Therefore, the correct equation is:
𝑑 = 48ℎ