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

w is the speed of the whale

c is the speed of the current

Against the current:

96 = 3 ( w-c)

32 = w-c <--- please label this equation APHA

With the current:

96 = 1.5 (w + c)

960 = 15(w + c)

320 = 5(w+c)

64 = w+c <--- please label this equation BETA

adding equations ALPHA + BETA:

96 = 2w

w = 48

this forces c = 16

CHECK:

with current: 1.5 ( 48 + 16) = 1.5(64) = 96

against current: 3( 48-16) = 3(32) = 96

The speed of the whale is 48 mph

the speed of the current is 16 mph

Answer 2

Suggest we use w for whale speed and c for current speed.

You will need to use a system of equations to answer this question:

(a) 3(w-c)=96 [subtract because it is going against the current]

(b) 1.5(w+c)=96 [add because it is going with the current]

If we expand these out, we get

(a) 3w-3c=96

(b) 1.5w+1.5c=96

we can multiply (b) by 2 to make it easier to add these two together so we get

(a) 3w-3c=96

(b) 3w+3c=192

Notice that 3c cancels out, so we get 6w=288 Divide both sides by 6 we get w=48

Hence, the speed of the whale is 32 mph.

We have a value for w so now we can just substitute that value to the equation (a) to find c

3(w-c)=96

3(48-c)=96

144-3c=96

144-96=3c

48=3c

16=c

Hence, the speed of the current is 16 mph.