A cabin cruiser traveling with the current went 12 mi in 1 h. Traveling against the current, it took 2 h to go the same distance. Find the rate of the cabin cruiser in calm water and the rate of the current
+128408 Call the rate of the current, C
Call the rate of the boat in still water, R
And with the current, the boat travels at a rate of R + C mph
And against the current the boat traravels at a rate of R - C mph
Rmember that Distance / Rate = Time
And time it took to travel 12 against the current = 1 hour more than with the current = 2 hours....so.....
12/ [ R + C ] = 1 multiply both sides by R + C
12 = R + C → 12 - R = C (1)
And against the current we have that
12/ ( R - C ) = 2
12 = 2(R - C) divide through by 2 and sub (1) in for C
6 = R - (12 - R)
6 = 2R- 12
18 = 2R divide both sides by 2
9 (mph) = R = rate in still water
And the rate of the current is 12 - 9 = 3 mph
