Question 1167287: A train travel from Tutuban to Calamba station. The distance between Tutuban and Calamba is defined by the function 𝑑(𝑥) = 𝑥4 + 𝑥3+ 3𝑥2 + 4𝑥 − 𝑥 kilometers. If the train travels from Tutuban to Calamba for 𝑡(𝑥) = 𝑥 hours without stopping at any station, do you think if the speed of this train will be 45 km/h, will it arrive on its destination for only 2 hours?
Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'm not sure if this is right, but i'll give it a shot, based on my understanding of the problem, or lack thereof.
you are given that:
d(x) = x^4 + x^3 + 3x^2 + 4x - x kilometers.
t(x) = x
presumably the same value of x is used in both equations.
what i think this means is, the distance traveled is a function of time traveled, and that this relationship is preserved for any given speed.
the formula i think you would want to use is:
r * t = d
r is the rate in kilometers per hour.
t is the time in hours.
d is the distance in hours.
based on the formulas you are given, this becomes:
r * t(x) = d(x)
if the train travels for 2 hours, then:
t(x) = x becomes t(2) = 2
d(x) = x^4 + x^3 + 3x^2 + 4x - x becomes d(2) = 2^4 + 2^3 + 3*2^2 + 4*2 - 2 which becomes d(2) = 42.
you have t(2) = 2 and d(2) = 42
if the trip takes 2 hours, then the distance traveled is 42 kilometers based on the value of x = 2 in both equations.
the rate * time = distance equation of r * t(x) = d(x) becomes:
r * 2 = 42
solve for r to get:
r = 42/2 = 21.
this says the train will travel 42 kilometers in 2 hours if the train travels at 21 kilometers per hour.
since 21 kilometers per hour is slower than 45 kilometers per hour, the train should make it in plenty of time.
in fact, assuming the distance is 42 kilometers and the train is traveling at 45 kilometers per hour, then the train will make the trip in 42/45 of an hour.
multiply this by 60 to find that the train travels for 56 minutes to go 42 miles.
i believe your solution is that the train will definitely make the trip in less than 2 hours with plenty of time to spare, based on my understanding of the problem.
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