Rate of current

Question

A whale is swimming against an ocean current traveled 60 mi in 2 hr. Swimming in the opposite direction, with the current, the whale was able to travel the same distance in 1.5 hr. Find the speed of the whale in calm water and the rate of the ocean current.

Answer 1

Hello T,

I am going to use the equation

Rate * Time = Distance

(R * T = D),

set up two equations,

and then solve by substitution.

 

Let r = the whale's rate in calm water, and

C = the rate of the current.

 

For the first sentence, swimming against the current will reduce my rate.  So

(r - C) * (2) = 60

→ r - C = 30

→ r = C + 30 {Eq 1}.

 

Then, swimming with the current will increase my rate,

→ (r + C) * (1.5) = 60,

→ r + C = 40 {Eq 2},

→ (C + 30) + C = 40 [by plugging in {Eq 1}],

→ 2C = 10

→ C = 5

→ r = 35 [by plugging into and solving {Eq 2}.

 

So the rate of the ocean current is 5 m/h and the speed of the whale in calm water is 35 m/h.

 

Thank you for the question.

Michael E.