Answer:
It will take Emma 7.4 hours to catch Mason.
Step-by-step explanation:
Let's build the equations of motion for both Mason and Emma, starting at the minute 48.
These equations have the following format:
[tex]S(t) = S(0) + vt[/tex]
In which S is the position after t minutes, S(0) is the initial position and v is the velocity, in miles per hour.
Mason
Mason walks at 3.7 mph. So [tex]v = 3.7[/tex].
48 minutes is 0.8 hour. So at 48 minutes, his position is 0.8*3.7 = 2.96. So S(0) = 2.96.
Mason's equation of motion is:
[tex]S_{M}(t) = 2.96 + 3.7t[/tex]
Emma
Emma starts at the position 0, with speed of 4.1mph. o
Emma's equation of motion is:
[tex]S_{E}(t) = 4.1t[/tex]
How long will it take Ema to catch up tp Mason ?
This will happen when they are at the same position. So
[tex]S_{M}(t) = S_{E}(t)[/tex]
[tex]2.96 + 3.7t = 4.1t[/tex]
[tex]0.4t = 2.96[/tex]
[tex]t = 7.4[/tex]
It will take Emma 7.4 hours to catch Mason.
