SOLUTION: A boat can travel 59 mph in still water. If it travels 130 miles with the current in the same length of time it travels 106 miles against the current, what is the speed of the cu

Algebra ->  Average -> SOLUTION: A boat can travel 59 mph in still water. If it travels 130 miles with the current in the same length of time it travels 106 miles against the current, what is the speed of the cu      Log On


   

Question 1057562: A boat can travel 59 mph in still water. If it travels 130 miles with the current in the same length of time it travels 106 miles against the current, what is the speed of the current ?
Found 3 solutions by josmiceli, addingup, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed of the current
+59+-+c+ = speed of the boat going against the current
+59+%2B+c+ = speed of the boat going with the current
Let +t+ = time in hrs going both with and against the current
--------------------------------------------------------------------
Going against the current:
(1) +106+=+%28+59+-+c+%29%2At+
Going with the current:
(2) +130+=+%28+59+%2B+c+%29%2At+
----------------------------
(1) +t+=+106+%2F+%28+59+-+c+%29+
Plug this result into (2)
(2) +130+=+%28+59+%2B+c+%29%2A%28+106+%2F+%28+59+-+c+%29%29+
(2) +130%2A%28+59+-+c+%29+=+106%2A%28+59+%2B+c+%29+
(2) +7670+-+130c+=+6254+%2B+106c+
(2) +236c+=+1416+
(2) +c+=+6+
The speed of the current is 6 mi/hr
------------------------------------
check:
(1) +t+=+106+%2F+%28+59+-+c+%29+
(1) +t+=+106+%2F+%28+59+-+6+%29+
(1) +t+=+106%2F53+
(1) +t+=+2+ hrs
and
+t+=+130+%2F+%28+59+%2B+c+%29+
+t+=+130+%2F+%28+59+%2B+6+%29+
+t+=+130+%2F+65+
+t+=+2+ hrs
OK

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the speed of the current.
Write the speed equation:
d = r*t; r = d/t
:
130/(59-x) = 105/(59+x) Expand the terms on both sides:
(59/130)-(x/130) = (x/105)+(59/105)Subtract (x/105) and (59/130) from both sides (hint: find common denominators)
:
-47x/2730 = 59/546 Now we've isolated the x on the left, solve for x by multiplying both sides by 2730/47:
:
x = 295/47 = 6.28 or 6.277 if you need 3 decimals is the speed of the current.
----------------------------------------------
Check:
59+6.277 = 65.277 and 130/65.277 = 2 hours
59-6.277 = 52.723 and 106/52.723 = 2 hours
We have the correct answer.
:
John



Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

A boat can travel 59 mph in still water. If it travels 130 miles with the current in the same length of time it travels 106 miles against the current, what is the speed of the current ?
Speed of current: