Current Speed

A boat took 3 hours to travel 24 km with the current. On the return trip, the boat took 5 hours to travel 24 km against the current. Determine the speed of the current.

 

Let  B  represent the rate of the boat in still water.

Let  C  represent the rate of the boat in still water.

 

The rate moving downstream is  B + C.

The rate moving upstream is       B - C

 

Distance  =  Rate x Time

Downstream:  24  =  (B + C)·3     --->   3B + 3C  =  24     --->   x 5    --->    15B + 15C  =  120

Upstream:       24  =  (B - C)·5     --->   5B  - 5C  =  24     --->   x -3   --->   -15B + 15C  =  -72

                                      Adding down the columns:                                                30C  =  48

                                                                                                                                    C  =  1.6

24/3=8 kmh-the speed of the boat with the current

24/5=4.8 kmh-the speed of the boat against the current

8 - 4.8 =3.2 kmh-difference in the speed of the boat due to current in coming and going.

3.2/2 =1.6 kph-speed of the current.