SOLUTION: During the rescue operations, the coast guard boat travel at a constant speed of 8
kilometers per hour in still water. In a river with unknown current, it takes the boat thrice as
Question 1171113: During the rescue operations, the coast guard boat travel at a constant speed of 8
kilometers per hour in still water. In a river with unknown current, it takes the boat thrice as long to travel 64 kilometers upstream (against the current) than it takes for 64 kilometers return trip (with the current). What is the speed of the current?
Against the current (upstream)
64- Distance
8-x - Speed
64 8−𝑥 - time
With the current (downstream)
64 -Distance
8+x -speed
64 8+𝑥 - Time Found 2 solutions by Boreal, greenestamps:Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website! time to go upstream is 64/(8-c) km/km/h =h
time to go downstream is 64/(8+c)
64/(8-c)=3*64/(8+c)
cross-multiply
512+64c=1536-192c
256c=1024
c=4 km/h
so it is 16 hours upstream and 5 1/3 hours downstream
The work you show in your post indicates you are going to use the distance of 64 miles, the speed of the boat in still water, and an unknown for the speed of the current, to find expressions for the times traveled upstream and downstream; then you will be able to answer the problem by solving the equation that says the upstream time is three times the downstream time.
That is a perfectly good method for solving the problem; and the other tutor has provided a solution using that method.
The work required to reach the answer is far less if a different approach is used.
The distances are the same, so if the upstream times is 3 times the downstream time, then the downstream speed is 3 times the upstream speed.