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.
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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