A cabin cruiser traveling with the current went 45 mi in 3 h. Traveling against the current it took 5H to go the same distance find the rate of the cabin cruiser in calm water and the rate of the current

      Rate of the cabin cruiser will be 12 miles per hour and the rate of the current is 3 miles per hour.

  Let the speed of the current = r miles per hour

And the speed of the cabin cruiser in the calm water = c miles per hour

Speed of the cabin cruiser against the current = (c - r) miles per hour

Speed of the cabin cruiser with the current = (c + r) miles per hour

Since, expression for the speed is given by,

Speed =

Therefore, speed of the cabin cruiser with the current = = 15 miles per hour

So the equation for the speed will be,

c + r = 15 ------ (1)

Time taken to cover 45 miles against the current = 5 hours

Therefore, equation for this situation will be,

c - r =

c - r = 9 ------- (2)

Now solve this system of equations,

Add equation (1) and (2),

(c + r) + (c - r) = 15 + 9

2c = 24

c = 12 miles per hour

Substitute the value of 'c' in equation (1),

12 - r = 9

r = 12 - 9

r = 3 miles per hour

     Therefore, speed of the cabin cruiser will be 12 miles per hour and the rate of the current is 3 miles per hour.

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the rate of the cabin cruiser in calm water is 12 mph.

the rate of the current is 3 mph.

Step-by-step explanation:

Let x represent the rate of the cabin cruiser in calm water.

Let y represent the rate of the current.

A cabin cruiser traveling with the current went 45 miles in 3 h. This means that the total speed is (x + y) miles per hour.

Distance = speed × time

Distance travelled with the current is

45 = 3(x + y)

Dividing through by 3, it becomes

15 = x + y - - - - - - - - - - -1

Traveling against the current it took 5 hours to go the same distance. This means that the total speed is

(x - y) miles per hour.

Distance travelled against the current is

45 = 5(x + y)

Dividing through by 5, it becomes

9 = x - y - - - - - - - - - - -2

Adding equation 1 to equation 2, it becomes

24 = 2x

x = 24/2

x = 12 mph

Substituting x = 12 into equation 1, it becomes

15 = 12 + y

y = 15 - 12

y = 3 mph

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step-by-step explanation: