Question 230564
Two sports cars leave the city at 9 a.m. One heads due south at 60 mph, the other car travels east at 45 mph. How far apart are they at noon?


Step 1.  The two cars travel for 3 hours since the difference between 12 and 9 is 3.


Step 2.  distance = speed * time


Step 3.  Let 60*3=180 be the distance of the car traveling south.


Step 4.  Let 45*3=135 be the distance of the car traveling east.


Step 5.  Let d be the distance that the cars are apart after 3 hours.


Step 6.  Use the Pythagorean Theorem to find the distance the two cars are apart after 3 hours.  The theorem states that the sum of the square of the legs of a right triangle is equal to the square of the hypotenuse ( distance the cars are apart in this example).


{{{d^2=180^2+135^2}}}


{{{d^2=32400+18225}}}


{{{d^2=50625}}}


Take the square root to both sides of the equation


{{{sqrt(d^2)=sqrt(50625)}}}


{{{d=225}}}


Step 7.  ANSWER:  The two cars will be 225 miles apart.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J