A boat's crew rowed 33kilometers downstream, with the current, in 3hours. The return trip upstream, against the current, covered the same distance, but took 11hours. Find the crew's rowing rate in still water and the rate of the current.

The crew rowing rate in still water = 7km/hr

The rate of the current = 4km/hr

Step-by-step explanation:

The distance rowed downstream with the current = 33km

Time taken to row downstream = 3hrs

The distance rowed upstream against the current = 33km

Time taken to row upstream = 11hrs

Let the crew's rowing rate in still water = Xkm/hr

Let the rate of current = Ykm/hr

For the downstream movement, we will have (X+Y). This is because the boat rowed with the current

For the upstream movement, we will have (X-Y). This is because the boat rowed against the current

Downstream Speed = distance / time

= 33/3

= 11km

Upstream speed = distance / time

= 33/11

= 3km

Hence X+Y = 11 and X-Y = 3

Add both equations. We have

X+Y+X-Y = 11 + 3

2X = 14

X = 14/2

X = 7

put X = 7 in any of the equations

7-Y = 3

Y = 7-3

Y = 4

Hence the crew rowing rate in still water = 7km/hr and the rate of the current = 4km/hr