SOLUTION: Car A passes point O heading east at a constant rate of 40 mph; Car B passes the same point one hour later heading north at a constant rate of 60 mph. Express the distance between
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Question 575458: Car A passes point O heading east at a constant rate of 40 mph; Car B passes the same point one hour later heading north at a constant rate of 60 mph. Express the distance between the cars as a function of time t, where t is measured starting when car B passes point O.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
At 
, A is 40 miles from O and B is at O. As time increases, A moves away from O at 40 mph, so at any positive time 
hours, A is 
miles from O. At the same time, B is 
miles from O, but in a direction at right angle to A's direction of travel.
Hence, the distance A has traveled at time is one leg of a right triangle and the distance B has traveled at the same time is the other leg of a right triangle.
With a tip of the hat to Mr. Pythagoras:
\ =\ \left((60t)^2\ +\ (40\ +\ 40t)^2\right)^{\frac{1}{2}})
You can simplify if you like.
John
My calculator said it, I believe it, that settles it
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