word problem

[loralja]

How long will it take a police officer to catch a motorist traveling at 60 miles per hour, if the police is 2 miles behind the motorist and is traveling 75 miles per hour?

Where do I start? How do I solve this?

 

[Denis]

P=Police, M=Motorist
P(@75)>----------2 miles--------------M(@60)>------------------? miles------------------>[P,M]
Formula: speed = distance / time

See how far you can get...

 

[BigGlenntheHeavy]

Note: Rate times Time = Distance

\(\displaystyle Motorist: \ 60 \ mph \ X \ t \ hrs. \ = \ 60t \ miles \ + \ 2 \ miles \ head \ start.\)

\(\displaystyle Cop: \ 75 \ mph \ X \ t \ hrs \ = \ 75t \ miles\)

\(\displaystyle Now, \ when \ the \ cop \ catches \ up \ to \ the \ motorist, \ there \ times \ are \ equal,\)

\(\displaystyle hence, \ 75t \ = \ 60t \ + \ 2, \ t \ = \ \frac{2}{15}hrs. \ = \ 8 \ minutes.\)

\(\displaystyle Therefore, \ in \ 8 \ minutes, \ the \ cop \ will \ have \ nabbed \ the \ motorist.\)

 

[Denis]

And, to the sounds of "Happy Trails To You", BigGlen and Loralja ride into the sunset.....