Problema Solution
Two cars leave an intersection. One car travels north; the other travels east. When the car traveling north had gone 24 miles, the distance between the cars was foyr miles more than three times the distance traveled by the car heading east. Find the distance between the cars at the time.
Answer provided by our tutors
there is a little spelling mistake in the text: we shell consider 'foyr' to be four.
d1 = 24 miles the distance passed by the car traveling north
d2 = the distance passed by the car traveling east
d = distance between the cars
the distance between the cars was four miles more than three times the distance traveled by the car heading east
d = 4 + 3*d2 => d2 = (d - 4)/3
since the paths of the cars are perpendicular we can use the Pythagorean Theorem
d1^2 + d2^2 = d^2 if we substitute for d2 = (d - 4)/3
24^2 + ((d - 4)/3) = d^2
by solving the quadratic equation we find the roots 25 and -26 and consider only the positive root since d>0
thus the distance between the cars was 25 miles.