SOLUTION: During the first part of a trip, a canoeist travels 42 miles at a certain speed. The canoeist travels 4 miles on the second part of the trip at a speed 5 mph slower. The total time
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-> SOLUTION: During the first part of a trip, a canoeist travels 42 miles at a certain speed. The canoeist travels 4 miles on the second part of the trip at a speed 5 mph slower. The total time
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Question 632320: During the first part of a trip, a canoeist travels 42 miles at a certain speed. The canoeist travels 4 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 4 hrs. What was the speed on each part of the trip? Answer by mananth(16946) (Show Source):
First Part x mph
Second Part x -5 mph
Total time 4 hours
First Part time 42 / x
Second Part time 4 / ( x -5 )
Time first part + time second part = 4 hours
42 / x + 4 /(x -5 ) = 4
LCD = ( x + 0 )* (x -5 )
multiply the equation by the LCD
we get
42 * (x+ -5 )+ 4 x = 4
42 x+ -210 + 4 x = 4 X^2 -20 x
66 x+ -210 = 4 X^2
4 X^2 -66 x+ 210 = 0
4 X^2+ -66 x+ 210 = = 0
/ 4
4 X^2 -66 x+ 210 = 0
Find the roots of the equation by quadratic formula
a= 4 b= -66 c= 210
b^2-4ac= 4356 - 3360
b^2-4ac= 996 = 31.56 OK 5
x1=( 66 + 31.56 )/ 8
x1= 12.19
x2=( 66 -31.56 ) / 8
x2= 4.31
x2 is not possible
so x= 12.2 mph first part of trip
7.2 mph second part of trip. (12.2-5)
