SOLUTION: A motorboat takes 5 hours to travel 200km going upstream. The return trip takes 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the

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Question 1065811: A motorboat takes 5 hours to travel 200km going upstream. The return trip takes 4 hours going downstream.
What is the rate of the boat in still water and what is the rate of the current?
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
A motorboat takes 5 hours to travel 200km going upstream. The return trip takes 4 hours going downstream.
What is the rate of the boat in still water and what is the rate of the current?
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200%2F5 = u - v   (1)   ( the speed upstream)

200%2F4 = u + v   (2)   ( the speeddownstream)

Or, which is the same,

u - v = 40,    (1')
u + v = 50.    (2')

Add equations (1') and (2') (both sides). You will get

2u = 50 + 40  ---->  2u = 90  ---->  u = 90%2F2 = 45.

The speed of the boat is 45 mph in still water.

The current speed is 5 mph.

Solved.

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".



Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Boat goes upstream at 40 km/h and downstream at 50 km/h
s-c upstream=40 km/h
s+c downstream=50 km/h
2s=90
s=45 km/h still water speed
c= 5 km/h