.
Let V be the speed of the stream (of the current), in km/h
Then the speed of the boat traveling downstream is (9+v) km/h,
while the speed of the boat traveling upstream is (9-v) km/h.
The time for traveling upstream is hours,
while The time for traveling downstream is hours.
Therefore, the time equation is
= 18 (total time).
Divide both sides by 18 and multiply both sides by (9-v)*(9+v). You will get
4(9+v) + 4*(9-v) = , or
= 81 - 2*36 = 9.
Therefore, v = 3 km/h is the rate of the current.
Answer. The rate of the current is 3 km/h.
It is a typical and standard Upstream and Downstream round trip word problem.
You can find many similar fully solved problems on upstream and downstream round trips with detailed solutions in lessons
- Wind and Current problems
- More problems on upstream and downstream round trips
- Selected problems from the archive on the boat floating Upstream and Downstream
in this site.
Read them attentively and learn how to solve this type of problems once and for all.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the section "Word problems", the topic "Travel and Distance problems".