SOLUTION: During the first part of a trip, a canoeist travels 75 miles at a certain speed. The canoeist travels 24 miles on the second part of the trip at a speed 5 mph slower. The total t
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-> SOLUTION: During the first part of a trip, a canoeist travels 75 miles at a certain speed. The canoeist travels 24 miles on the second part of the trip at a speed 5 mph slower. The total t
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Question 130883: During the first part of a trip, a canoeist travels 75 miles at a certain speed. The canoeist travels 24 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hours. What was the speed on each part of the trip?
The speed on the first part of the trip was ____ mph.
The speed on the second part of the trip was ____ mph.
You can put this solution on YOUR website! Distance(d)=Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=speed for first part of trip
Then r-5=speed on second part of trip
Time required for first part of trip= d/r=75/r
Time required for second part of trip=d/r=24/(r-5)
Now we are told that the sum of the above two times equals 5 hours, so:
75/r+24/(r-5)=5 multiply each term by r(r-5)
75(r-5)+24r=5r(r-5) get rid of parens
75r-375+24r=5r^2-25r subtract 5r^2 from and add 25r to both sides
75r-375+24r-5r^2+25r=5r^2-5r^2-25r+25r collect like terms
-5r^2+124r-375=0 multiply each term by -1
5r^2-124r+375=0 quadratic in standard form. Solve using quadratic formula mph------speed on first part of trip mph---speed on second part of trip
mph--------------speed on second part of trip (NO!!!)
r-5=3.535-5=NEGATIVE VALUE NO GOOD!!!!
CK
75/21.275 + 24/16.275=5
3.525+1.474=5
4.999999--~~~~5
