SOLUTION: A motorboat takes 5 hours to travel 100 miles going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate

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Question 1148597: A motorboat takes
5 hours to travel
100 miles going upstream. The return trip takes
2 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, Alan3354:
Answer by ikleyn(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let "u" be the rate of the boat in still water,

and let "v" be the rate of the current.


Then

    u + v = 100%2F2 = 50 mph is the effective rate moving downstream, and

    u - v = 100%2F5 = 20 mph is the effective rate moving upstream.


Add the equations to get 


    2u = 50+20 = 70 mph,   u = 70/2 = 35 mph.


Substitute the found value of "u" into the first equation to get


    v = 50 - 35 = 15 mph.


ANSWER.   The rate of the motorboat in still water is 35 mph; the rate of the current is 15 mph.

Solved.

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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
    - Wind and Current problems solvable by quadratic equations
    - Unpowered raft floating downstream along a river
    - Selected problems from the archive on the boat floating Upstream and Downstream
in this site, where you will find other similar solved problems with detailed explanations.

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".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A motorboat takes 5 hours to travel 100 miles going upstream.
The return trip takes 2 hours going downstream.
What is the rate of the boat in still water and what is the rate of the current?
---------------
b = speed of the boat
c = current
==============
A motorboat takes 5 hours to travel 100 miles going upstream.
b - c = 100/5 = 20 mi/hr
-----
The return trip takes 2 hours going downstream.
b + c = 100/2 = 50 mi/hr
---
b - c = 20 mi/hr
b + c = 50 mi/hr
-------------------------- Add