truck moves oils (lubricating oil presumably) to gas stations.
At full load the truck transportation cost is 300$ when the traveling distance is 120km
and the transportation cost is 350$ when the traveling distance is 165km
At this interval, the costs change linearly. You may use calculater for aid.
a) calculate the cost when the distance traveled is 150km
b) assuming the cost and distance change linearly even beyond the original interval, calculate the new distance, for when the cost would be 1000$
c) when do the costs fall, below 2$ per kilometer
k = deltay/deltax
The Attempt at a Solution
equation for straight line is of the form
Also it should be noted that the costs do actually grow, when the distance traveled actually grows... there was something fishy about the ratio though. I think we must probably find the correct constant value for the b term in the equation
y= k * x + b
k= (350-300) / (165- 120)
it is said that the interval has linear growths, I think we should probe the starting value, to see what the constant b would have been
300 = (10/9) * 120 + b
y=( 10/3 ) * x + (500/3)
probe for the end value in interval (assuming end point and beginnning point are within the interval)
we achieve y= 350
When the values x= 165 and k= 10/9 and b = 500/3 is used
a) cost = 333,33 , distance traveled = 150km
b) cost = 1000$ distance traveleld = 750km
c) I need help for this part I think
My teacher sent me the different answers as mine. She sent me the answers to these.
Teacher had calculated k = (350-300) / (165-120) = 9/10
Correspondingly teacher had different value for the b term.
I don't think you end up with 9/10 = 50/45 in any mathematical fashion right there... but I don't know.
I think earlier my math teacher said that brackets are calculated first.
(350-300) / (165-120) = 50/45
50/45 fraction can be shrunken without changing its value ( I don't know what the procedure is called in English language, but fractions can shown in different forms, without changing its value, when you multiply or divide both the numeratorr and denominator by the same number which would not be 0)
10/ 9 = 50/45
because 50/5= 10
45/ 5 = 9
The question clearly stated that the costs change linearly with the distance travellled.
Cost grows, and distance grows. I don't think it is possible that the cost and the distance are inversely correlated between each other.
I'm pretty confused about whether or not my teacher was correct or whether I was correct.
I could use help to the c part of the problem.
How do I make sure that I find when the cost per km, drops to below (2$ / km)?