SOLUTION: Two fishing boats depart a harbor at the same time, one traveling east, the other south. The eastbound boat travels at a speed 7 mi/h faster than the southbound boat. After five ho

Algebra ->  Triangles -> SOLUTION: Two fishing boats depart a harbor at the same time, one traveling east, the other south. The eastbound boat travels at a speed 7 mi/h faster than the southbound boat. After five ho      Log On


   

Question 467078: Two fishing boats depart a harbor at the same time, one traveling east, the other south. The eastbound boat travels at a speed 7 mi/h faster than the southbound boat. After five hours the boats are x = 85 mi apart. Find the speed of the southbound boat.
I came up with 5mph being the speed of the slower boat, but the EWA says I'm wrong
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the courses of the two boats form a right triangle with the 85 mi separation being the hypotenuse

the eastbound boat is 7 mph faster for 5 hr, so it travels 35 mi more than the southbound boat

if d is the southbound distance, by Pythagoras ___ d^2 + (d + 35)^2 = 85^2

2d^2 + 70d + 35^2 - 85^2 = 0 ___ d^2 + 35d - 3000 = 0 ___ (d + 75)(d - 40) = 0

d + 75 = 0 ___ d = -75 , negative value not realistic

d - 40 = 0 ___ d = 40 ___ 40 mi in 5 hr is 8 mph