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

Answer 2

The speed of the boat is 9 miles per hour and the speed of the water is 7 miles per hour.

Let us assume the actual speed of the boat is x miles per hour and  the actual speed of the water is y miles per hour.

A boat goes 32 miles downstream in two hours.

Downstream means the boat is flowing in the direction of the river flow.

Thus,

The formulated way to represent the distance traveled by any object is mentioned below:

$\rm{Distance}=Speed \times Time$

Now, put our current conditions in that and make an expression of x and y.

Thus,

$32=(x+y) \times 2\\(x+y)=16$

The return trip against the current takes sixteen hours.

The return trip is the upstream, therefore the boat is flowing in the opposite direction of the river flow.

Thus,

The formulated way to represent the distance traveled by any object is mentioned below:

$\rm{Distance}=Speed \times Time$

Now, put our current conditions in that and make an expression of x and y.

Thus,

$32=(x-y)\times 16\\x-y=2$

Solving both the expressions we get x equals to 9 miles per hour and y equals to 7 miles per hour.

Thus, the speed of the boat is 9 miles per hour and the speed of the water is 7 miles per hour.

To know more about the downstream, please refer to the link:

https://brainly.com/question/3421273