Question

A motor boat can travel 45 km downstream in 2 h and 30 min; and 39 km upstream in 3 h and 15 min. What is the speed of the boat in still water? What is the speed of the current?

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Answer 1

c = speed of current = 3 km/hr

r = speed of boat in still water = 15 km/hr

Explanation:

Use the formula distance = time x rate to set up these equations

45 = 2.5 (r+c)

39 = 3.25 (r-c)

(r + c) is the speed of the boat added to the speed of the current, downstream

(r - c) is the speed of the boat minus the speed of the current, upstream

Use one equation to isolate a variable then substitute it into the other equation to solve the system.

39/3.25 = r - c

12 + c = r

45 = 2.5 ( 12 + c + c )

18 = 12 + 2c

6 = 2c

c = 3

Then use the equation 12 + c = r from above

12 + c = r

12 + 3 = 15

r = 15 km/hr