SOLUTION: a fishing boat broke down after traveling 2 hours against a 4 km/h current. The boat was carried back to its starting point by the current. The whole trip took 5.5 hours. Find the

Algebra ->  Test -> SOLUTION: a fishing boat broke down after traveling 2 hours against a 4 km/h current. The boat was carried back to its starting point by the current. The whole trip took 5.5 hours. Find the      Log On


   

Question 240637: a fishing boat broke down after traveling 2 hours against a 4 km/h current. The boat was carried back to its starting point by the current. The whole trip took 5.5 hours. Find the speed of the boat in still water before the motor failed.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
d = distance the boat travelled.

boat travels for 2 hours against a 4 km/h current.

the whole trip took 5.5 hours which means the boat drifted back for 3.5 hours.

distance the boat travels against the current is equal to:

d = (b-4)*2

distance the boat drifts with the current is equal to:

d = (4)*3.5 = 14 miles

since the distance getting to the point where the boat broke down and getting back is the same distance, the formula for the boat getting to that point becomes:

14 = (b-4)*2

remove parentheses to get:

14 = 2b-8

add 8 to both sides to get:

2b = 22

divide both sides by 2 to get:

b = 11

Speed of the boat should be 11 miles per hour.

plug into the original equations to confirm this value is good.

first equation is boat getting to the breakdown point:

(b-4)*2 = d

replace d with 14 and b with 11 to get:

(11-4)*2 = 14 becomes: 7*2 = 14 becomes 14 = 14 confirming equation 1 is true.

second equation is boat drifting back to the starting point:

d = 4*3.5 becomes:

14 = 4*3.5 becomes 14 = 14 confirming e4quation 2 is true.

values look good.

speed of the boat in still water before breaking down is 11 miles per hour.

basic formula used is:

rate * time = distance