A boat can travel 48 miles upstream in 4 hours...

Question

A boat can travel 48 miles upstream in 4 hours. The return trip takes 3 hours. Find the speed of the boat in still water and the speed of the current.

Answer 1

rate * time = distance

b = speed of boat

c = speed of current

upstream going against current

downstream going with current

upstream (b - c) * 4 = 48

downstream (b + c) * 3 = 48

create simultaneous equations:

4b - 4c = 48

3b + 3c = 48

multiply equations so can cancel one of the variables:

12b - 12c = 144

12b + 12c = 192

Add two equations together and solve for b:

24b = 336

b = 14

substitute b = 14 into one of the equations and solve for c:

3(14) + 3c = 48

3c = 6

c = 2

speed of boat is 14; speed of current is 2