SOLUTION: A barge moves 6km/h in still water. It travels 51 km upriver and 51 km downriver in a total time of 114 hr. What is the speed of the current?

Question 415415: A barge moves 6km/h in still water. It travels 51 km upriver and 51 km downriver in a total time of 114 hr. What is the speed of the current?
Answer by sheldonxu(4) (Show Source): You can put this solution on YOUR website!
Let the speed of the current X.
When the barge is traveling downriver, its net speed equals to the sum of the speed of the barge in still water and the speed of the current. That is, (X+6) km/h.
When the barge is traveling upriver, its net speed equals to the difference of the speed of the barge in still water and the speed of the current. That is (X-6)
km/h.
According to the time formula: time=distance/speed, you can set up an equation:
51/(X+6) + 51/(X-6) = 114
time spent in downriver time spent in upriver total time
solve by multiplying (X-6)(X+6) to each side of the equation:
(X-6)(X+6)*51/(X+6) + (X-6)(X+6)*51/(X-6) = 114*(X-6)(X+6)
reduce and simplify:
51*(X-6) + 51*(X+6) = 114(X^2-36)
51*X-6*51 + 51*X +6*51 = 114*(X^2) - 114*36
Move every item to right side and combine like terms:
114*(X^2) -102*X -114*36=0
Simplify by reducing a 6:
19*(X^2) - 17X - 684 =0
Use the formula

you can get two answers, one is negative, not suitable in this case. The other is
(17+sqrt(52273))/38=6.46 (rounded to the nearest hundredth)
So, the speed of the current is 6.46km/h.

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