SOLUTION: I am very confused by the problem below, mostly once you get the common denominator. What do you do after you get that to complete the problem? We were shown an example, but it was

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Question 612723: I am very confused by the problem below, mostly once you get the common denominator. What do you do after you get that to complete the problem? We were shown an example, but it was not very explanatory. Any helpful tips would be much appreciated. Thanks!!!
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During the first part of a trip, a canoeist travels 49 miles at a certain speed. The canoeist travels 4 miles on the second part of the trip at a speed of 5 mph slower. The total time for the trip is 2 hours. What was the speed on each part of the trip?

Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
t = d / r ___ the total time is 2 hr

2 = (49 / x) + [4 / (x - 5)]

the common denominator is the product of the two denominators
___ change the denominator of a fraction by multiplying by the missing factor, divided by itself; eg. [(x - 5) / (x - 5)]
___ a quantity divided by itself equals one; multiplying by one does not change the value of the fraction

2 = (49 / x)[(x - 5) / (x - 5)] + [4 / (x - 5)](x / x)

2 = {[49(x - 5)] / [x(x - 5)]} + {[4(x)] / [x(x - 5)]}

2[x(x - 5)] = 49(x - 5) + 4(x)

2x^2 - 10x = 53x - 245 ___ 2x^2 - 63x + 245 = 0

use the quadratic formula to find x

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
During the first part of a trip, a canoeist travels 49 miles at a certain speed.
The canoeist travels 4 miles on the second part of the trip at a speed of 5 mph slower.
The total time for the trip is 2 hours.
What was the speed on each part of the trip?
:
Let s = speed on the 1st 49 mi
then
(s-5) = speed on the 2nd part (4 mi)
:
Write a time equation: time = dist/speed
:
+ = 2
Multiply by s(s-5)
s(s-5)* + s(s-5)* = 2s(s-5)
Cancel the denominators
49(s-5) + 4s = 2s^2 - 10s
49s - 245 + 4s = 2s^2 - 10s
53s - 245 = 2s^2 - 10s
Combine as a quadratic equation on the right
0 = 2s^2 - 10s - 53s + 245
2s^2 - 63s + 245 = 0
We have to use the quadratic formula to find s

In this problem; x=s; a=2; b=-63; c= 245

Two solutions, but only one will make sense
s ~ 26.955 mi for the 1st 49 mi
then
26.955 - 5 = 21.955 mph for the last 4 mi
:
:
Confirm this; find the time with these solutions
+ = 2