SOLUTION: during the first part of a kayak trip jack covered 60 km at certain speed he then travel 24 km at a speed that was for kilometers an hour slower if the total trip was eight hours w
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Question 1004170: during the first part of a kayak trip jack covered 60 km at certain speed he then travel 24 km at a speed that was for kilometers an hour slower if the total trip was eight hours what was the speed on each part of the trip Found 2 solutions by ankor@dixie-net.com, addingup:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! during the first part of a kayak trip jack covered 60 km at certain speed
he then travel 24 km at a speed that was four kilometers an hour slower
if the total trip was eight hours, what was the speed on each part of the trip
:
let s = the speed for the 1st 60 km of the trip
then
(s-4) = the speed on the last 24 km
:
Write a time equation; time = dist/speed
fast time + slower time = 8 hrs + = 8
multiply equation by s(s-4), cancel the denominators and you have
60(s-4) + 24s = 8s(s-4)
60s - 240 + 24s = 8s^2 - 32s
84s - 240 = 8s^2 - 32s
Combine to form a quadratic equation on the right
0 = 8s^2 - 32s - 84s + 240
8s^2 - 116s + 240 = 0
simplify, divide equation by 4
2s^2 - 29s + 60 = 0
You can use the quadratic formula to solve a=2; b=-29; c=60
But this will factor to
(2s - 5)(s - 12) = 0
Two solutions
2s = 5
s = 2.5
and
s = 12 km/hr, this makes sense
:
:
Confirm this by finding the actual time at each speed
60/12 = 5 hrs
24/8 = 3 hrs (4 km/hr slower)
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total 8 hrs
You can put this solution on YOUR website! We will call the speed r (stands for rate, another word for speed)
60/r+24/r-4= 8 The common denominator is r*r-4, let's bring the numbers together:
(12(7r-20))/r(r-4)= 8 Multiply both sides by r(r-4):
12(7r-20)= 8r^2-32r Multiply on left
84r-240= 8r^2-32r Subtract right from left:
-8r^2+116r-240=0 Factor:
-4(r-12)(2r-5)=0 Divide by -4:
(r-12)(2r-5)= 0 Break it into 2 equations:
r= 12 or 2r= 5= r= 5/2 Let's try 12:
60/12= 5
24/(12-4)= 3
5+3= 8 hours The correct answer is 12km/h during the first part and 8km/h after that
