SOLUTION: Tony'a outboard can drive her boat at 7mph in still water. It takes her 10 minutes more to reach her friends camp 4 miles up the river than to return to her camp down river. What

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Question 761851: Tony'a outboard can drive her boat at 7mph in still water. It takes her 10 minutes more to reach her friends camp 4 miles up the river than to return to her camp down river. What is the speed of the current?
I have already asked this question on here before but got an incorrect answer. Be aware that it takes Tonya 10 minutes MORE not just 10 minutes. Here is my attempt
going: 4=(7-c)*(t+10) returning: 4=(7+c)*t
$=(7-c)*((4/7+c)+10)
Where do I go from here? You are so wonderful thank you so much!
Forever in debt to strangers, Abby
Found 3 solutions by josmiceli, Alan3354, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed of the current
+7+-+c+ = her speed going against the current
+7+%2B+c+ = her speed going with the current
Let +t+ = her time going with the current
+t+%2B+10+ = her time going against the current
-------------------------
Against the current:
(1) +4+=+%28+7+-+c+%29%2A%28+t+%2B+10+%29+
With the current:
(2) +4+=+%28+7+%2B+c+%29%2At+
-------------------
(1) +4+=+7t+-+c%2At+%2B+70+-+10c+
(1) +7t+-+c%2At+=+10c+-+66+
(1) +t%2A%28+7+-+c+%29+=+10c+-+66+
(1) +t+=+%28+10c+-+66+%29+%2F+%28+7-c+%29+
and
(2) +4+=+%28+7+%2B+c+%29%2At+
(2) +t+=+4%2F%28+7+%2B+c+%29+
By substitution:
(1) +4%2F%28+7+%2B+c+%29+=+%28+10c+-+66+%29+%2F+%28+7-c+%29+
Multiply both sides by +%28+7%2Bc+%29%2A%28+7-c+%29+
(1) +4%2A%28+7-c+%29+=+%28+10c+-+66+%29%2A%28+7%2Bc+%29+
(1) +4%2A%28+7-c+%29+=+2%2A%28+5c+-+33+%29%2A%28+7%2Bc+%29+
(1) +14+-+2c+=+35c+-+231+%2B+5c%5E2+-+33c+
(1) +5c%5E2+%2B+4c+-+245+=+0+
Use quadratic formula
+c+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+5+
+b+=+4+
+c+=+-245+ ( not the same c as current )
+c+=+%28-4+%2B-+sqrt%28+4%5E2+-+4%2A5%2A%28-245%29+%29%29+%2F+%282%2A5%29+
+c+=+%28-4+%2B-+sqrt%28+16+%2B+4900%29%29+%2F+10+
+c+=+%28-4+%2B-+sqrt%28+4916%29%29+%2F+10+
+c+=+%28-4+%2B+70.114+%29%2F+10+
+c+=+66.114+%2F+10+
+c+=+6.611+
The speed of the current is 6.611 mi/hr
check:
(2) +4+=+%28+7+%2B+c+%29%2At+
(2) +4+=+%28+7+%2B+6.611+%29%2At+
(2) +4+=+13.611t+
(2) +t+=+.294+
and
(1) +4+=+%28+7+-+6.611+%29%2A%28+t+%2B+10+%29+
(1) +4+=+.389t+%2B+3.89+
(1) +.389t+=+.11+
(1) +t+=+.283+
This method should be OK, but it doesn,t
exactly check- maybe you can find error
Hope this helps






Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Tony'a outboard can drive her boat at 7mph in still water. It takes her 10 minutes more to reach her friends camp 4 miles up the river than to return to her camp down river. What is the speed of the current?
--------------
The speed is in mi/hr, so change 10 mins to 1/6 hour
-----------
c = current
d = r*t
4 = (7-c)*(t + 1/6) = (7+c)*t
7t - ct -c/6 + 7/6 = 7t + ct
That won't work
==============================================
---------------
t = 4/(7+c)
t + 1/6 = 4/(7-c)
----
Sub for t
4/(7+c) + 1/6 = 4/(7-c)
(24 + 7 + c)/(6(7+c)) = 4/(7-c)
(31 + c)*(7-c) = 24(7+c)
-c^2 + -24c + 217 = 24c + 168
c^2 + 48c - 49 = 0
(c-1)*(c+49) = 0
c = 1 mi/hr

Answer by MathTherapy(10809) About Me  (Show Source):
You can put this solution on YOUR website!
Tony'a outboard can drive her boat at 7mph in still water. It takes her 10 minutes more to reach her friends camp 4 miles up the river than to return to her camp down river. What is the speed of the current?
I have already asked this question on here before but got an incorrect answer. Be aware that it takes Tonya 10 minutes MORE not just 10 minutes. Here is my attempt
going: 4=(7-c)*(t+10) returning: 4=(7+c)*t
$=(7-c)*((4/7+c)+10)
Where do I go from here? You are so wonderful thank you so much!
Forever in debt to strangers, Abby

Tony'a outboard can drive her boat at 7mph in still water. It takes her 10 minutes more to reach her friends camp 4 miles up the river than to return to her camp down river. What is the speed of the current?

Distance each way: 4 miles

Let speed of current = C

Speed up-river = 7 - C

Speed down-river = 7 + C

Time it takes to travel up-river: 4%2F%287+-+C%29

Time it takes to travel down-river: 4%2F%287+%2B+C%29

Since it takes 10 minutes, or 10%2F60, or 1%2F6 hr more to go up-river, then we can say that: 4%2F%287+-+C%29+-+1%2F6+=+4%2F%287+%2B+C%29

Solve this equation and you should get C, or speed of current to be highlight_green%281%29 mph

You can do the check!!

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