Question 468776: Two cars started from a junction at sametime. One went straight west and other straight north. The car that went westward travelled 10 km faster per hour than the other. After 1 hour distance between two cars is 15 km. Calculate the distance covered by the car that went northward. Also find the distance covered by car that went southward.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Two cars started from a junction at sametime. One went straight west and other straight north. The car that went westward travelled 10 km faster per hour than the other. After 1 hour distance between two cars is 15 km. Calculate the distance covered by the car that went northward. Also find the distance covered by car that went southward.
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I will assume you meant the last word above to be westward instead of southward.
After 1-hour:
Distance = speed*travel time
Let x=km traveled by car traveling north
x+10=km traveled by car traveling west
You now have a right triangle with legs of x and x+10 and a hypotenuse of 15 km
By the Pythagorean Theorem:
x^2+(x+10)^2=15^2=225
x^2+x^2+20x+100=225
2x^2+20x-125=0
Solving by quadratic formula
a=2, b=20, c=-125
x=[-20ħsqrt(20^2-4*2*-125]/2*2
x=[-20ħ√1400]/4
x=(-20ħ37.41)/4
x=-14.35 (reject, x>0)
or
x= 4.35
x+10=14.35
ans:
distance covered by car that went north=4.35 km
distance covered by car that went west=14.35 km
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