Question

A boat goes 32 miles downstream in two hours. The return trip againts the current takes sixteen hours. Find the rate of the boat in calm water and the rate of the current. ​

Answer 1

Answer: the rate of the boat in calm water is 9 mph and the rate of the current is 7 mph

Step-by-step explanation:

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

Let y represent the rate of the current.

A boat goes 32 miles downstream in two hours. Assuming that it travelled in the direction of the current, its total speed would be

x + y mph

Distance = speed × time

Distance covered downstream is

32 = 2(x + y)

16 = x + y - - - - - - - - - - - -1

The return trip against the current takes sixteen hours.

Its total speed would be x - y mph

Distance = speed × time

Distance covered on return trip is

32 = 16(x - y)

2 = 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

16 = 9 + y

y = 16 - 9 = 7 mph