Question 240637
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