Traviling upstream on the mississippi river, a barge travels 56 mi in 7 h. downstream, it travels the same distance in 4 h. find the rate of the barge in still water and the rate of the current

the speed of the barge in still water is 11 mph

the speed of the current is 3 mph

Step-by-step explanation:

Let x represent the speed of the barge in still water.

Let y represent the speed of the current.

Traveling upstream on the Mississippi River, the barge travels 56 mi in 7 h. This is against the water current. It means that the total speed of the barge would be

x - y mph

Distance = speed × time

Therefore,

56 = 7(x - y)

8 = x - y - - - - - - - - - - - -1

Downstream, it travels the same distance in 4 h. This is in the same direction with the water current. It means that the total speed of the barge would be

x + y mph

Therefore,

56 = 4(x + y)

14 = x + y - - - - - - - - - - - -2

Adding equation 1 and equation 2, it becomes

22 = 2x

x = 22/2 = 11

Substituting x = 11 into equation 2, it becomes

14 = 11 + y

y = 14 - 11 = 3

for the free

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