The speed of the current when it takes the boat 3 hours to travel upstream but only 2 hours to travel the same distance downstream is 25mph.
Given to us
Speed of the boat = 5 mph
It takes the boat 3 hours to travel upstream
2 hours to travel the same distance downstream
Let the distance traveled by boat be L.
We know that when the boat is going upstream the water current will provide resistance to the boat, therefore,
[tex]L = (S_c-S_b)\times T_u[/tex]
where L is the distance traveled by boat, [tex]\rm S_c\ and\ S_b[/tex] are the speed of current and boat respectively, And [tex]T_u[/tex] is the time of the boat during the downstream journey.
[tex]L = (S_c-5)\times 3[/tex]
We know that when the boat is going downstream the water current will provide help to the boat, therefore,
[tex]L = (S_c+S_b)\times T_d[/tex]
[tex]L = (S_c+5)\times 2[/tex]
We already have two-equation for the distance traveled by boat therefore, we will equate both the equations,
[tex](S_c-5)\times 3 = (S_c+5)\times 2[/tex]
[tex]3S_c-15= 2S_c+10\\\\3S_c-2S_c = 10+15\\\\S_c = 25\rm\ mph[/tex]
Hence, the speed of the current when it takes the boat 3 hours to travel upstream but only 2 hours to travel the same distance downstream is 25mph.
Learn more about Speed:
https://brainly.com/question/7359669
