SOLUTION: a cruise boat travels 84 miles downstream in 2 hours and returns upstream in 6 hours find the rate of the stream

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: a cruise boat travels 84 miles downstream in 2 hours and returns upstream in 6 hours find the rate of the stream       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 83625: a cruise boat travels 84 miles downstream in 2 hours and returns upstream in 6 hours find the rate of the stream
Found 3 solutions by checkley75, josmiceli, JohnsenP:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
D=RT OR R=D/T OR 84/2 OR 42 MPH DOWNSTREAM.
R=84/6 OR 14 MPH UPSTREAM.
(42-14)/2=28/2=14 MPH FOR THE CURRENT.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
s = rate of stream
b = rate of boat
For downstream:
d+=+%28b+%2B+s%29%2At
For upstream:
d+=+%28b+-+s%29%2At
84+=+%28b+%2B+s%29%2A2
84+=+2b+%2B+2s
--------------------
84+=+%28b+-+s%29%2A6
84+=+6b+-+6s
Multiply the 1st equation by 3
and add to the second
252+=+6b+%2B+6s
84+=+6b+-+6s
336+=+12b
b+=+28 This is the speed of the boat in still water in mph
84+=+2b+%2B+2s
84+=+2%2A28+%2B+2s
2s+=+84+-+56
2s+=+28
s+=+14Rate of stream in mph

Answer by JohnsenP(4) About Me  (Show Source):
You can put this solution on YOUR website!
Formula is D = r x t

Down stream = r + c
Upstream = r - c

Distance = 84 mile w/c is the same in both Up and Downstream

Time = Up 6 hrs
Time = Down 2 hrs

The equation is;

84 = (r + c)* 2 Downstream
84 = (r - c)* 6 Upstream

(84 = 2r + 2c)*-3 ( since you want to solve for the current, eliminate r
84 = 6r - 6c by multiplying -3)

-252 = -6r - 6c
84 = 6r - 6c

It yields -168 = -12 c devide both by -12 to get the value of c

c = 14 mph that's the speed of the stream

Hope this will help you. Johnsen P