Question 1009854
rate * time = distance
let a = the rate of the boat
let b = the rate of the current.


with the current, the rates are additive.
against the current, the rate are subtactive.


going with the current, rate * time becomes:


(a + b) * 3 = 24


going agains the current, rate * time becomes:


(a - b) * 4 = 16


simplify these equations to get:


3a + 3b = 24
4a - 4b = 16


multiply both sides of the first equation by 4 and multiply the second equation by 3 to get:


12a + 12b = 96
12a - 12b = 48


add the equations together to get:


24a = 144


solve for a to get a = 6


your original equations are:


(a + b) * 3 = 24
(a - b) * 4 = 16


replace a in the first equation to get:


(6 + b) * 3 = 24
distribute the multiplication to get:
18 + 3b = 24
subtract 18 from both sides to get:
3b = 6
solve for b to get:
b = 2


you have a = 6 and b = 2
this means the rate of the boat is 6 mph and the rate of the current is 2 mph.


go back to your original equations again and replace a with 6 and b with 2 to get:


(a + b) * 3 = 24 becomes (6+2) * 3 = 24 which becomes 8*3 = 24 which becomes 24 = 24.


(a - b) * 4 = 16 becomes (6-2) * 4 = 16 which becomes 4 * 4 = 16 which becomes 16 = 16.


this confirms the solutions are correct.


the rate of the boat is 6 miles per hour.
the rate of the current is 2 miles per hour.