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Question 1085275: Natasha leaves school at 3pm and she drives north at 40 km/hr. 2 hours later (at
5pm), Alli leaves and she drives East at 50 km/hr. How long does it take before the
two cars are 300 km apart?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Those are two legs of a right triangle whose hypotenuse is 300 and its square is 90,000
Natasha is going north at 40 km/hr. If time after 3 pm is x, her distance is 40x and the square is 1600x^2.
Alli is going at 50 kn/hr and travels (x-2) hours, so that her distance is 50x-100 km, square is 2500x^2-10000x+10000
Those two add to 90,000
so 4100x^2-10000x+10000=90000
4100x^2-10000x-80000=0
41x^2-100x-800=0
x=(1/82)(100+/- sqrt (10000+131200); sqrt(141200)=375.77
x=475.77/82=5.8 hours or 232 km , and square of that is 53824
x-2=3.8 hours or 190 km, and square of that is 36100
They add to 89924; using thousandths, the sum is 89999.13
The time will be 8:48 pm
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