calculus word problem - related rates

Question

two people leave the same point at the same time. one walks due east at a rate of 3 miles per hour. the other one walks due north at 2 miles per hour. find the rate at which the distance between them is increasing after they have been walking for 30 minutes

Answer 1

East 3 mph after 30 minutes is 1.5 miles (Let it be a)

North 2 mph after 30 minutes is 1 mile (Let it be b)

the triangle formed with sides = 1.5 & 1 with the hypotenuse (c) = sqrt(1.5² + 1²) = 1.803

a² +b² = c² Taking the derivative, we have 2a da + 2b db = 2c dc (dc is the unknown), then

2(1.5)(3) + 2(1)(2) = 2(1.803) dc

then dc = 3.606 mph