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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?

Sagot :

thebecks

Answer:

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 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

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