David M. answered 05/03/20
Dave "The Math Whiz"
We have 2 unknowns, so we need 2 equations to solve this.
Let x = speed of the boat in calm water
y = speed of the current
Eq. 1: The speed of the boat + the speed of the current means that it traveled 28 miles in 3.5 hours:
3.5(x + y) = 28
(x + y) = 28/3.5 = 8
Eq. 2: The speed of the boat - the speed of the current means that it traveled 12 miles in 3 hours:
3(x - y) = 12
(x - y) = 12/3 = 4
Using the elimination method, we can add Eq. 1 & 2 and solve for x:
x + y = 8 Eq. 1
+ x - y = 4 Eq. 2
2x = 12
x = 6
Plugging this value for x back into either Eq. 1 or 2 we can solve for y:
x + y = 8 Eq. 1
6 + y = 8 substitute for x
y = 8 - 6 subtract 6 from both sides
y = 2
Therefore, the speed of the boat in calm water is x = 6 mph and the speed of the current is y = 2 mph.
Hope this helps!