Question

Mason starts walking from home at 3.7 mph. Ema leaes to follow

Answer 1

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:

$S(t) = S(0) + vt$

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 $v = 3.7$.

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:

$S_{M}(t) = 2.96 + 3.7t$

Emma

Emma starts at the position 0, with speed of 4.1mph. o

Emma's equation of motion is:

$S_{E}(t) = 4.1t$

How long will it take Ema to catch up tp Mason ?

This will happen when they are at the same position. So

$S_{M}(t) = S_{E}(t)$

$2.96 + 3.7t = 4.1t$

$0.4t = 2.96$

$t = 7.4$

It will take Emma 7.4 hours to catch Mason.