Answer:
Speed of current is 3 miles per hour.
Step-by-step explanation:
Speed of boat without current, u = 13 miles/hr
Let speed of current = v miles/hr
Speed upstream = (13 - v) miles/hr
Speed downstream = (13 + v) miles/hr
Distance traveled upstream, [tex]D_1[/tex] = 80 miles
Distance traveled downstream, [tex]D_2[/tex] = 80 miles
Total time taken, T ([tex]T_1+T_2[/tex]) = 13 hours
Formula for Total Time taken:
[tex]Time= \dfrac{Distance}{Speed}[/tex]
Time taken in Upstream:
[tex]T_1 = \dfrac{80}{13-v}\ hours[/tex]
Time taken in Downstream:
[tex]T_2 = \dfrac{80}{13+v}\ hours[/tex]
[tex]T = T_1+T_2 = 13\ hours\\\Rightarrow 13 = \dfrac{80}{13-v}+\dfrac{80}{13+v}\\\Rightarrow 13 = 80(\dfrac{13+v+13-v}{13^2-v^2})\\\Rightarrow 13^2-v^2 = \dfrac{80(26)}{13}\\\Rightarrow 169-v^2 = 80\times 2\\\Rightarrow v^2 = 169-160 = 9\\\Rightarrow v = 3\ miles/hr[/tex]
So, speed of current is 3 miles/hr
