Kinematics Test Question: Can You Solve This Sheriff and Robber Pursuit Problem?

[zach5681b]

1. Ok so on my Pre-Calculus test today, there was a problem dealing with kinematics, I am in Physics so no problem right?... well teacher says otherwise. The question goes.
A Robber heads down a strait road at 10mph. 12 minutes later the Sherriff heads off in hot pursuit at 14mph. How long will it take the Sherriff to catch the thief.



2. so first things first. I set it up using D=RT (simple right). I set it up as
d=10*t + (10*.2) and d=14*t




3. Then i combined them to set equal to each other. 10*t +(10*.2)=14*t

Then I used my 89 and got .5 or 30 min as my answer.


But the problem is my teacher set it up like this.

10t=14(t-1/5)

and he got .7 as the answer.



Any help who can tell which is right, because I have a feeling you can't do what my teacher did.

This will make my C on the Test to a B if i am right and the teacher is wrong...does anyone know

 

[krausr79]

You are correct. Granted, my first reaction would be to set it up like your teacher; however if you check the answers:

10*.5 = 5 miles
10*.2 = 2 miles
14*.5 = 7 miles

the distances are the same

10*.7 = 7 miles
10*.2 = 2 miles
14*.7 = 9.8 miles

the distances are different

Show your teacher this:
10*(t+1/5) = 14t
and tell him that this method (the equivalent of yours) gives the robber a 12 minute head start while his method
10t = 14(t-.2)
gives the sheriff a 12 minute un-head start at the sheriff's rate of speed.

14*.2 = 2.8

The sheriff's un-head start is worth the extra .8 miles.

Subtle!

 

[Gib Z]

Well, there is a simple way to check the answers without doing the problem again. The Robber has a 12 minute head start, whilst running at 10mph. So he is obviously 2 miles ahead. Now to test your solution, you say 1/2 an hour. So how far has the Sheriff gotten in 30minutes? Obviously 7 miles. How far has the Robber gotten? Another 5 miles, plus the 2 head start. Both result in having traveled 7 miles. So you answer is obviously correct.

EDIT: Ooh, only seconds before me lol.