Question

A train travels 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, how fast is the train traveling?

Answer 1

given :

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.

distance traveled is a function of time traveled, and that this relationship is preserved for any given speed.

Formula

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) = t(2) = 2

d(x) = x^4 + x^3 + 3x^2 + 4x - x

d(2) = 2^4 + 2^3 + 3*2^2 + 4*2 - 2

d(2) = 42.

hence, 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)

r × 2 = 42

r = 42/2

= 21.

this says the train will travel 42 kilometers in 2 hours if the train travels at 21 kilometers per hour.