Let the velocity of boat in still water = b and velocity of river = r

Downstream velocity = b + r = 27/3 = 24 mph

Upstream velocity = b - r = 60/10 = 10 mph

Adding the above two equations we get 2b = 24 + 10 = 34

So b 34/2 = 17 mph. Plugging this value into the first equation we get

17+ r = 24 ; r = 24 - 17 = 7 mph

Answer is the river flows at 7 miles per hour and the boat goes in still water at the rate of 17 miles per hour

or

If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are?

:

Let s = speed of the boat, & c = current

Speed upstream = (s-c)

Speed downstream = (s+c)

:

Two unknowns, two distance equation, Dist = time * speed

:

3(s + c) = 72

Simplify divide equation by 3:

s + c = 24

And:

6(s - c) = 60

Simplify divide equation by 6

s - c = 10

:

Use the elimination method on these two simplified equations

s + c = 24

s - c = 10

----------------adding eliminates c

2s = 34

s = 34/2

s = 17 mph boat speed

:

Find the current:

s + c = 24

17 + c = 24

c = 24 - 17

c = 7 mph is the current.

:

;

Check our solutions in: 3(s + c)= 72 and 6(s-c) = 60

3(24) = 72

and

6(10) = 60