P and Q are 12 miles far from each other.
Given that
Patrick drives from P to Q at an average speed of 40 mph
Also he drives from Q to P at an average speed of 45 mph
Let "s" be the distance between P and Q in miles.
Let "t" be the time in minutes
There are 60 minutes in 1 hours
[tex]\rm So \;in \; "t" \; minutes \; there\; will\; be = \dfrac{t}{60} \ hours[/tex]
By the definition pf average speed we can write that
[tex]\rm Average \; Speed = \dfrac{Total \; distance }{Total \; time}\\[/tex]
The speed is given in two situations in miles per hour
Case 1 When average speed = 40 mph
[tex]\rm 40 = \dfrac{s}{t/60} \\\\\rm {40 = \dfrac{60s}{t} .....(1) }[/tex]
Case 2 When average speed = 45 mph
Given that Patrick takes two minutes less
[tex]\rm 45 = \dfrac{s}{(t-2)/60} \\\\45 = \dfrac{60s}{t-2 } ....(2)[/tex]
Solving for "s" from equations (1) and (2) gives us
[tex]\rm \bold {s = 12}}[/tex]
So we can conclude that P and Q are 12 miles far from each other.
For more information please refer to the link given below
https://brainly.com/question/21470320
