Question

Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. 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 and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?(1) Train B arrived in New York before Train A arrived in Boston.(2) The distance between New York and Boston is greater than 140 miles.

Answer 1

Time of arrival of train B is 4:20 PM

Step-by-step 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

`t_A=(s)/(100)`

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

`v=(s-100)/(0.167)=6(s-100)=6s-600`

Time taken by train B

`t_B=(s)/(v)=(s)/(6s-600)`

The combined travel time of the two trains is 2 hours

That is

`t_A+t_B=(s)/(100)+(s)/(6s-600)=2\\\\6s^2-600s+100s=1200s-120000\\\\6s^2-1700s+120000=0\\\\\texttt{s = 150 miles or s = 133.33 miles}`

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

`t_B=(150)/(6* 150-600)=0.5hours`

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