Respuesta :
Time of arrival of train B is 4:20 PM
Explanation:
Let the distance between New York and Boston be s.
Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph.
Time taken by train A
[tex]t_A=\frac{s}{100}[/tex]
An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM
At 4:00 PM combined distance by them is s.
Let the speed of train B be v.
We have
100 x 1 + v x 0.167 = s
[tex]v=\frac{s-100}{0.167}=6(s-100)=6s-600[/tex]
Time taken by train B
[tex]t_B=\frac{s}{v}=\frac{s}{6s-600}[/tex]
The combined travel time of the two trains is 2 hours
That is
[tex]t_A+t_B=\frac{s}{100}+\frac{s}{6s-600}=2\\\\6s^2-600s+100s=1200s-120000\\\\6s^2-1700s+120000=0\\\\\texttt{s = 150 miles or s = 133.33 miles}[/tex]
Given that the distance between New York and Boston is greater than 140 miles.
So the distance is 150 miles.
Time taken by train B
[tex]t_B=\frac{150}{6\times 150-600}=0.5hours[/tex]
Time of arrival of train B = 3:50 PM + 0.5 hours = 4:20 PM
Time of arrival of train B is 4:20 PM
