Question

After sailing 14 mi, a sailor changed direction and increased the boat's speed by 4 mph. An additional 15 mi was sailed at the

increased speed. The total sailing time was 3 h. Find the rate of the boat for the first 14 mi.

Answer 1

14/r + 15/(r + 4) = 3

14(r + 4) + 15r = 3r(r + 4)

14r + 56 + 15r = 3r² + 12r

29r + 56 = 3r² + 12r

3r² - 17r - 56 = 0

(r - 8)(3r + 7) = 0

r = 8 mph

For the first 14 miles, the speed of the boat was 8 mph.