Question 1146100
r * t = d
r = rate
t = time
d = distance


b = the rate of the boat
c = the rate of the current


going with the current, r = b + c
going against the current, r = b - c


your formulas become:


with the current:
(b + c) * t = d


against the current:
(b - c) * t = d


d - 259 nukes
t = 13 hours going with the current.
t = 26 hours going against the current.


your formulas become:


with the current:
(b + c) * 13 = 260


against the current:
(b - c) * 26 = 260


simplify both formulas to get:
13b + 13c = 260
26b - 26c = 260


these two equations need to be solved simultaneously.


multiply both sides of the first equation by 2 and leave the second equation as is to get:
26b + 26c = 520
26b - 26c = 260


add both equations together to get:
52b = 780


solve for b to get:
b = 780/52 = 15


in the first of the two equations, replace b with 15 and solve for c.
start with 13b + 13c = 260
replace b with 15 to get 13*15 + 13c = 260
simplify to get 195 + 13c = 260
subtract 195 from both sides to get:
13c = 65
solve for c to get c = 65/13 = 5


replace b with 15 and c with 5 in both original equations to get:
13b + 13c = 13*15 + 13*5 = 195 + 65 = 260
26b - 26c = 26*15 - 26*5 = 390 - 130 = 260


b = 15 and c = 5 are confirmed to be good values.
your solution is that the rate of the boat is 15 miles per hour and the rate of the current is 5 miles per hour.