THIS EXURSION WITH A BOAT TRAVEL 35KM UPSTREAM AND THEN BACK AGAIN IN 4 H 48 MINUTRE. iF THE SPEED OF THE BOAT I5 K,/H, WHAT IS THE SPEED OF THE CURRENT?
Let v be the speed of the current. The boat's speed upstream (relative to the land) is 15-v and the speed downstream is 15+v. The total trip time is
35/(15-v) + 35/(15 + v) = 4.8 (hours)
Solve for the single unknown, v.
900
To solve for the speed of the current, we can start by setting up the equation using the given information.
Let v be the speed of the current. The boat's speed upstream (relative to the land) would then be 15 - v, and the speed downstream would be 15 + v.
Since the total trip time is 4 hours and 48 minutes, we need to convert this to hours. There are 60 minutes in an hour, so 48 minutes is equivalent to 48/60 = 0.8 hours.
Now we can set up the equation:
35/(15 - v) + 35/(15 + v) = 4.8
To solve this equation, we need to find a common denominator and then combine the fractions on the left side:
35(15 + v) + 35(15 - v) = 4.8(15 - v)(15 + v)
Expanding both sides of the equation:
35(15 + v) + 35(15 - v) = 4.8(225 - v^2)
Simplifying:
525 + 35v + 525 - 35v = 1080 - 4.8v^2
Combining like terms:
1050 = 1080 - 4.8v^2
Rearranging the equation:
4.8v^2 = 1080 - 1050
4.8v^2 = 30
Dividing both sides of the equation by 4.8:
v^2 = 6.25
Taking the square root of both sides:
v = ±2.5
Since the speed of the current cannot be negative, the speed of the current is 2.5 km/h.