SOLUTION: Can somebody walk me through a step on this quadratic word problem? A small motorboat travels 13 mph in still water. It takes 2 hours longer to travel 60 miles going upstream

Algebra.Com
Question 1042685: Can somebody walk me through a step on this quadratic word problem?

A small motorboat travels 13 mph in still water. It takes 2 hours longer to travel 60 miles going upstream than it does going downstream. Find the rate of the current.

I am at a point where I have:
60/13-x - 60/13+x =2
I know that I need to multiply both sides of the equation by the LCD and that it will turn into:
2x^2+20x-338=0
But I just cant seem to figure out HOW to actually do that. I think the denominators of 13-x/13+x are really throwing me.
Or if somebody has an easier way to get to the quadratic equation in this word problem I am all ears.
Thanks so much in advance!
Found 4 solutions by ikleyn, Boreal, ankor@dixie-net.com, stanbon:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
A small motorboat travels 13 mph in still water. It takes 2 hours longer to travel 60 miles going upstream
than it does going downstream. Find the rate of the current.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

 = 

Multiply both sides of the equation by (13-x)*(13+x) 

60*(13+x) - 60*(13-x) = ,

120x =     <--- Your mistake was here.

2x^2 + 120x - 338 = 0,

x^2 + 60x - 169 = 0.   

Can you complete it from this point ?


Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
The speed upstream is 13-c, where c is the current.
The time it takes is 60/(13-c), as you have with units mi/mi/hr, with units hr.
The time it takes to go downstream is 60/(13+c), and that is 2 hours less than upstream
Therefore, 60/(13-c)-2=60/(13+c)
Your LCD is (13-c)(13+c)
60(13+c)-2(169-c^2)=60(13-c)
780 +60c-338+2c^2=780-60c
780 cancels,
2c^2+120c-338=0; Notice, this is 120c, not 20c.
divide by 2
c^2+60c-169=0
c=(1/2)(-60+/-sqrt (3600+676) sqrt (4276)=65.39
use positive root (1/2)5.39=2.695 mph
Upstream speed is 10.305 mph
Downstream speed is 15.695 mph
60/10.305=5.822 hours
60/15.695=3.822 hours
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
A small motorboat travels 13 mph in still water.
It takes 2 hours longer to travel 60 miles going upstream than it does going downstream.
Find the rate of the current.
:
You are definitely on the right track. Here it is step by step anyway.
:
let = the rate of the current
then
(13+r) = the effective speed down stream
and
(13-r) = the effective speed upstream
:
Write a time equation, time = dist/speed
Time upstream - time downstream = 2hr
- = 2
multiply the equation by the common denominator
(13-r)(13+r)* - (13-r)(13+r) = 2(13-r)(13+r)
Cancel the denominators, FOIL on the right (difference of squares)
60(13+r) - 60(13-r) = 2(169-r^2)
distribute
780 + 60r - 780 + 60r = 338 - 2r^2
Combine like terms to form a quadratic equation on the left
2r^2 + 120r - 338 = 0
simplify, divide by 2
r^2 + 60r - 169 = 0
Using the quadratic formula; a=1; b=60; c=-169, I got solutions of of
r = - 69.7
and
r = 2.7 mph is the rate of the current (the positive solution is all we want)
:
:
:
See if this checks out by finding the actual time each way, Subtract and add the current from 13
60/10.3 = 5.825 hrs
60/15.7 = 3.822 hrs
--------------------
difference 2 hrs (discrepancy from me rounding off the original solutions)
:
:
Did this make sense to you. Let me know in the comment CK
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
A small motorboat travels 13 mph in still water. It takes 2 hours longer to travel 60 miles going upstream than it does going downstream. Find the rate of the current.
-----
I am at a point where I have:
60/(13-x) - 60/(13+x) =2
--------
60(13+x) - 60(13-x) = 2(169-x^2)
----------------------------
120x = 2*169 - 2x^2
2x^2+120x-2*169 = 0
---------------------------
x^2 + 60x - 169 = 0
----------------------
x = [-60 +- sqrt(3600-4*-169)]/(2)
-----
Positive solution::
x = 2.32 mph
--------------
Cheers,
Stan H.
------------

RELATED QUESTIONS

I need help setting up this word problem into a equation. Problem: Jen's motorboat... (answered by josgarithmetic)
A small motorboat travels 15 mph in still water. It takes 1 hour longer to travel 72... (answered by Boreal)
A motorboat travels upstream at 7 mph, while it travels downstream at 12 mph. What is the (answered by lwsshak3)
Can you help me solve this math problem: A man can drive a motorboat 45 miles down the... (answered by scott8148)
Hello Tutors, Please help me solve this rational expression word problem. When... (answered by josgarithmetic)
Can you help me figure out this problem? "A motorboat travels at 4 miles per hour in... (answered by richwmiller)
please help me solve this problem in quadratic equation; 1.a motorboat takes 4 hours to... (answered by stanbon)
A motorboat at full throttle takes two hours longer to travel 75 miles against the... (answered by scott8148)
i am a sophmore in highschool taking PreCal and i need help. I have to write a 50 word... (answered by longjonsilver)