Boat stream calculation problems

Question

Q1. A person rows to a place 48 km distant and back in 14 hours. The person can row 4 km with the stream in the same time as 3 km against the stream. What is the rate of the stream?

Q2. In a stream running at 2 km/h, a motor boat goes 10 km up stream and back again at the starting point in 55 minutes. Find the speed of the motor boat in still water.

Answer 1

Q₂. 55 min = 55/60 = 11/12 hours.

Then x + 2 = 10/(11/12); x = 120/11 - 2 = 98/11 km/h;

Q₁. 4/(x + y) = 3/(x - y)

48/(x + y) + 48/(x - y) = 14

From 1st equation 3x + 3y = 4x - 4y; x = 7y

48/(8y) + 48/(6y) = 14; 6/y + 8/y) = 14; 14/y = 14; y = 1 km/h