Answer: Because the speed of the train that travels 30 miles in [tex]\frac{1}{3}[/tex] hour is greater than the speed of the other train.
See explanation.
Step-by-step explanation:
The formula to find the constant speed is:
[tex]V=\frac{d}{t}[/tex]
Where "V" is the constant speed, "d" is the distance and "t" is the time.
Knowing that a train travels 30 miles in [tex]\frac{1}{3}[/tex] hour at a constant speed, we can identify that:
[texd=30\ mi\\t=\frac{1}{3}\ h[/tex]
Substituting these values into the formula, we get that the constant speed of this train is:
[tex]V_1=\frac{30\ mi}{\frac{1}{3}\ h}\\\\V_2=90\ \frac{mi}{h}[/tex]
The other train travels 20 miles in [tex]\frac{1}{2}[/tex] hour at a constant speed, then we can identify that:
[texd=20\ mi\\t=\frac{1}{2}\ h[/tex]
Substituting values into the formula, we get that the constant speed of the this train is:
[tex]V_2=\frac{20\ mi}{\frac{1}{2}\ h}\\\\V_2=40\ \frac{mi}{h}[/tex]
Since [tex]V_1>V_2[/tex] , we can conclude that the train travels 30 miles in [tex]\frac{1}{3}[/tex] hour at a constant speed, is faster than the other train.
