Question

A motorboat traveling 310 km in five hours going upstream and 736 km in eight hours going down stream what is the rate of the boat in Stillwater and what is the rate of the current

Answer 1

Solution

For this case we can create the following notation

B= velocity of boat

S= velocity of stream

Relative to the bank, the speed upstream is B-S.

The speed downstream is B+S.

And we can create the following equations:

(B-S)*5= 310

(B+S)*8= 736

We can solve for B and S and we have:

5B -5S = 310

8B+ 8S= 736

B= (310+5S)/5= 62+ S

Replacing in the second equation we got:

8(62+S) + 8S= 736

496 + 8S + 8S = 736

16S= 240

S= 240/16= 15

B= 62+15= 77

Then the velocity of current is 15km/hr and for the boat 77km/hr