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A woman paddling a canoe downstream with the river current travels 28 miles in 2 hours. On the return trip, she paddles the same distance upstream against the river current in 7 hours. Write and solve a system of two linear equations to determine the rate of the boat in calm water and the rate of the current, both in miles per hour.

Respuesta :

Answer: the rate of the boat in calm water is 9 mph and the rate of the current is 5 mph

Step-by-step explanation:

Let x represent the rate of the boat in calm water.

Let y represent the rate of the current.

The woman paddling a canoe downstream with the river current travels 28 miles in 2 hours. Assuming that she paddled in the direction of the current, her total speed would be x + y mph

Distance = speed × time

Distance covered downstream is

28 = 2(x + y)

14 = x + y - - - - - - - - - - - -1

On the return trip, she paddles the same distance upstream against the river current in 7 hours.

Assuming that she paddled against the direction of the current, her total speed would be x - y mph

Distance = speed × time

Distance covered upstream is

28 = 7(x - y)

4 = x - y - - - - - - - - - - - -2

Adding equation 1 and equation 2, it becomes

18 = 2x

x = 18/2 = 9 mph

Substituting x = 9 into equation 1, it becomes

14 = 9 + y

y = 14 - 9 = 5 mph

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