After sailing 18 mi, a sailor changed direction and increased the boat's speed by 4 mph. An additional 13 mi was sailed at the increased speed. The total sailing time was 3 h. Find the rate of the boat for the first 18 mi.

Solution

A f t er s ai l in g 18 mi, a s ai l or c han g e d d i rec t i o n an d in cre a se d t h e b o a t^{'} s s p ee d b y 4 m p h . A n a dd i t i o na l 13 mi w a s s ai l e d a t t h e in cre a se d s p ee d . T h e t o t a l s ai l in g t im e w a s 3 h . F in d t h e r a t e o f t h e b o a t f or t h e f i rs t 18 mi .

trip 1 speed : 9

trip 2 speed : 13

Solution steps

Translate the problem into an equation:

\frac{18}{x} + \frac{13}{x + 4} = 3

Solve for

x, \frac{18}{x} + \frac{13}{x + 4} = 3 : x = 9, x = - \frac{8}{3}

Find speed

trip 1 speed : 9

trip 2 speed : 13