Question

50 POINTS AND BRAINLIEST :))
Two cars left at an intersection at the same time, one heading south and the other heading east. Later they were exactly 95 miles apart. The car heading west had gone 38 miles less than twice as far as the car heading south. How far had each traveled?

Answer 1

Hi buddy

Here is your answer

Answer 2

This is a problem where pythagoras theorem has to be applied

at any given time the cars are travelling at right angles to each other

north bound has traveled x miles

west bound car traveled 2x-38miles

leg1^2+leg2^2=hypotenuse ^2

x^2+(2x-38)^2=95^2

x^2+4x^2-152x+1444=9025

5x^2-152x-7581=0

Find the roots of the equation by quadratic formula

a= 5 , b= -152 , c= -7581

b^2-4ac= 23104 + 151620

b^2-4ac= 174724 %09sqrt%28%09174724%09%29=%09418%09

x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29

x1=( 152 + 418 )/ 10

x1= 57.00

x2=( 152 -418 ) / 10

x2= -26.60

Ignore negative value

57 miles north bound car

west bound car = 2*57-38=76 miles