SOLUTION: A crew rowed 7 miles upstream in 2 hours and the 6 1/2 miles downstream in 1 hour. Find the rate of the crew in still water and the rate of the current.

Algebra.Com
Question 1111037: A crew rowed 7 miles upstream in 2 hours and the 6 1/2 miles downstream in 1 hour. Find the rate of the crew in still water and the rate of the current.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
--------------------------------------------------------------------------
A crew rowed 7 miles upstream in 2 hours and the 6 1/2 miles downstream in 1 hour. Find the rate of the crew in still water and the rate of the current.
----------------------------------------------------------------------

---------------------------------------------------------------
A crew rowed U miles upstream in h hours and the D miles downstream in k hour. Find the rate of the crew in still water and the rate of the current.
---------------------------------------------------------------

r, speed of crew if no current
c, speed of the current
U=7
D=6.5
h=2
k=1


-
and

You can just substitute the values to compute r and c.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Let "u" be the speed of the boat in still water (in mph)

and "v" be the speed of the current.



Then the effective speed upstream is

u - v = 3.5  mph    (1)      (=7/2 mph)



while the effective speed downstream is  

u + v = 6.5  mph    (2)      (from the condition)



Adding (1) and (2), you find  2u = 3.5+6.5 = 10  ====>  u = 5 mph.



Then  from (2),  v = 6.5 - 5 = 1.5 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
    - 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.

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.


RELATED QUESTIONS

A crew rows 4 miles downstream and 2 miles upstream in one hour. Then it rows 6 miles... (answered by mananth)
A boat's crew rowed 12 miles downstream, with the current, in 2 hours. The return trip... (answered by Alan3354)
a boat crew rowed 20 miles downstream with the current in 2 hours. the return trip... (answered by Alan3354)
a boat crew rowed 16 miles downstream with the current in 2 hours . the return trip... (answered by checkley77)
a boats crew rowed 18 miles downstream with the current in 2 hrs the return trip upstream (answered by mananth)
Please help me solve this word problem equation A boat's crew rowed 12 miles... (answered by checkley77)
A crew rowing with the current traveled 16 miles in 2 hours; against the current, the... (answered by josmiceli)
Flying through the wind a plane flew 420 miles in 3 hours. Against the current, the crew... (answered by Alan3354,ikleyn)
A boat travels 16 1/2 miles upstream and 18 miles downstream in 9 hrs. It then travels... (answered by mananth)