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.
