Find the speed of the whale and current

Question

A whale swimming against an ocean current traveled 160 mi in 5 h. Swimming in the opposite direction, with the current, the whale was able to travel the same distance in 2.5 h. Find the speed of the whale in calm water and the rate of the ocean current.

Answer 1

160 miles in 5 hours up stream

160 miles in 2.5 hours down stream

distance = rate of speed times time traveled

d=rt

160 = (r+c)2.5 = (r-c)5 where c= the speed of the ocean water, and r = speed of the whale in still calm water

5r - 5c = 160

2.5r+2.5c = 160

multiply the 2nd equation by 2 and add to the 1st

5r + 5c = 320

5r - 5c = 160

10r =480

r= 480/10 = 48 mph = whale's speed in calm water

5c = -160+5(48) = -160+240= 80

c= 80/5 = 16 mph= ocean speed

48-16 = 32 mph. 32 x5 = 160

48+16 = 64mph 64x2.5 = 160