Find the speed of the whale in calm water and the rate of the ocean current.

Question

A whale swimming against an ocean current traveled 96 mi in 3 h. Swimming in the opposite direction, with the current, the whale was able to travel the same distance in 1.5 h. Find the speed of the whale in calm water and the rate of the ocean current.

whale ______mph

current _____mph

Answer 1

We have 2 unknowns, so we need 2 equations to solve this.

Let x = speed of whale in calm water

y = speed of the current

Eq. 1: In 3 hours the whale swims against the current and travels 96 miles:

3(x - y) = 96

x - y = 96/3

x - y = 32

Eq. 2: In 1.5 hours the whale swims the same distance with the current:

1.5(x + y) = 96

x + y = 96/1.5

x + y = 64

Adding Eq. 1 & 2 together we can solve for x:

x - y = 32 Eq.1

+ x + y = 64 Eq. 2

2x = 96

x = 96/2

x = 48

Using this value for "x" in either Eq. 1 or 2 we can solve for "y":

x - y = 32 Eq. 1

48 - y = 32 substitute for "x"

48 -32 = y subtract 32 and add "y" to both sides

16 = y

Therefore, the whale is swimming at 48 mph in calm water and the current is flowing at 16 mph.

Hope this helps!

Answer 2

96 = 3 ( x-y) = 3x - 3y

96 = 1.5(x+y) = 1.5x + 1.5y

1.5x - 4.5y = 0

1.5x = 4.5y

x = 3y

96 = 3(3y-y) = 6y

y = 16

x = 48

whale 48 ocean current 16