The number of miles Abigail’s boat travels, m, varies directly with the amount of time Abigail spends boating, t. If she spends 2 h in her boat, she travels 19 mi. How do you model this with a direct linear variation?

Question

Ethan Adkins · Accepted Answer

#m=19/2t# #"the initial statement is "mpropt# #"to convert to an equation multiply by k the constant"# #"of variation"# #m=kt# #"to find k use the given condition"# #t=2,m=19# #m=ktrArrk=m/t=19/2# #"equation is "m=19/2t#

Jameson Allen · Answer

undefined The direct linear variation model for this scenario is represented by the equation: $m = kt$, where $m$ is the number of miles Abigail's boat travels, $t$ is the amount of time Abigail spends boating, and $k$ is the constant of variation. Given that Abigail travels 19 miles when she spends 2 hours in her boat, you can find $k$ by solving for it in the equation $19 = k \times 2$. Thus, $k = \frac{19}{2}$. So, the equation that models this direct linear variation is $m = \frac{19}{2}t$.