SOLUTION: Heather's boat has a top speed of
6
miles per hour in still water. While traveling on a river at top speed, she went
10
miles upstream in the same amount of time she went
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Question 1046114: Heather's boat has a top speed of
6
miles per hour in still water. While traveling on a river at top speed, she went
10
miles upstream in the same amount of time she went
30
miles downstream. Find the rate of the river current.
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the speed of the curent in mi/hr
= her speed going upstream
= her speed going downstream
Let = her time in hrs for both trips
---------------------------------------
Going upstream:
(1)
Going downstream:
(2)
---------------------
(1)
Plug (1) into (2)
(2)
(2)
(2)
(2)
(2)
The rate of the current is 3 mi/hr
----------------------------------
check:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
boat has a top speed of 6 miles per hour in still water.
While traveling on a river at top speed, she went 10 miles upstream in the same amount of time she went 30 miles downstream.
Find the rate of the river current.
:
let c = the rate of the current
then
(6-c) = effective speed upstream
and
(6+c) = effective speed downstream
:
Write a time equation; time = dist/speed
:
time up = time down
=
cross multiply
10(6+c) = 30(6-c)
distribute
60 + 10c = 180 - 30c
10c + 30c = 180 - 60
40c = 120
c = 120/40
c = 3 mph is the rate of the current
:
:
:
Check this; find the actual time each way
10/(6-3) = 3.33 hrs
30/(6+3) = 3.33 hrs
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