Two cars are starting at the same point. One car starts driving north at a constant speed of 25mph. Two hours later, the other car drives east at a constant speed of 20mph. How long until the cars are 300 miles apart?

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Answer 1 · 2018-06-13T07:45:38

Let after #t# hrs of starting of 1st car the distance between two cars becomes #300# miles.

So displacement of 1st car towards North #25t# mile

And the displacement of 2nd car towards East #20t-40# mile.

#(25t)^2+(20t-40)^2=300^2#

#=>1025t^2-1600t-90000+1600=0#

#=>1025t^2-1600t-88400=0#

#=>41t^2-64t-3536=0#

#=>t=(64+sqrt(64^2+4*41*3536))/82#

#=>t~~10.1# hr