Patrick drives from P to Q at an average speed of 40 mph . His drive back from Q to P is at an average speed of 45 mph and takes two minutes less. How far, in miles, is it from P to Q?

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

By the definition pf average speed we can write that

The speed is given in two situations in miles per hour

Case 1  When average speed = 40 mph

Case 2 When  average speed = 45 mph  

Given that Patrick takes two minutes less  

Solving for "s" from equations (1) and (2) gives us

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

link

Distance=12 miles

Step-by-step explanation:

d=distance

t=time going

d/t=40 mph going

t-2/60=time returning      (2 minutes/60 minutes per hour)

d/(t-2/60)=45 mph returning

set up equations:

d=40t

d=45(t-2/60)

substitute:

40t=45(t-2/60)

40t=45t-90/60

40t=45t-3/2

0=5t-3/2

5t=3/2

t=0.3 hours or 18 minutes

(time returning=16 minutes)

substitute:

d=40t=40(0.3)

d=12 miles

p

step-by-step explanation:

-3.5 is the distance.

i've had this question so choose the one in the absolute value sign.