guys the 7 th one plz
Answers
Answer:
6 km/hr
Step-by-step explanation:
Let v > 0 be the speed of the water current in km/hr.
The speed of the boat when going with the current is then 12 + v, so the time taken to travel the 36 km in that direction is
time₁ = distance / speed = 36 / ( 12 + v ).
The speed of the boat when going against the current is 12 - v, so the time taken to travel the 36 km in that direction is
time₂ = distance / speed = 36 / ( 12 - v ).
The total time is taken is 8 hours, so...
time₁ + time₂ = 8
=> 36 / ( 12 + v ) + 36 / ( 12 - v ) = 8
=> 9 / ( 12 + v ) + 9 / ( 12 - v ) = 2
=> 9 ( 12 - v ) + 9 ( 12 + v ) = 2 ( 12 + v ) ( 12 - v )
=> 108 - 9v + 108 + 9v = 2 ( 12² - v² )
=> 2×108 = 2 ( 144 - v² )
=> 108 = 144 - v²
=> v² = 144 - 108 = 36
=> v = 6 ( since v > 0 ).
So the speed of the water current is 6 km/hr.