Question

A transit train from Boston to New York and a passenger train from New York to Boston departed at the same time, at $3:00\mathrm{PM}$ . The distance between New York station and Boston station is $280\mathrm{miles}$. The speed of the transit train was $80\mathrm{miles}\mathrm{per}\mathrm{hour}$. The speed of the passenger train was $60\mathrm{miles}\mathrm{per}\mathrm{hour}$. At what time will the trains pass each other?

Answer 1

To find the time when both trains pass each other.

The distance between New York station and Boston station is $280\mathrm{miles}$.

The speed of the transit train was $80\mathrm{miles}\mathrm{per}\mathrm{hour}$. The speed of the passenger train was $60\mathrm{miles}\mathrm{per}\mathrm{hour}$.

Let $\text{t}$ be the time when both trains pass each other.

Using the relative speed formula.

Let, $\text{D}=280\text{miles}$, ${\text{s}}_1=80\text{miles per hour}$ and ${\text{s}}_2=60\text{miles per hour}$ .

Since both trains are going to close, so the speed of the trains will be add.

Now using the relative speed formula in below:

$\begin{array}{rcl}\text{time}\left(\text{t}\right)& =& \frac{\text{Distance}\left(\text{D}\right)}{\text{Relative speed}\left({\text{s}}_1+{\text{s}}_2\right)}\left(\text{Relative speed formula}\right)\\ & \Rightarrow & \text{t}=\frac{280}{80+60}\left(\text{Substitute the all values}\right)\\ & \Rightarrow & \text{t}=\frac{280}{140}\left(\text{Add denominator}\right)\\ \therefore \text{t}& =& 2\left(\text{Divide}\right)\end{array}$

Therefore, both trains will meet in $2\mathrm{hours}$.

Since both trains departed at the same time, at $3:00$ PM, so both trains will meet at $3+2=5\text{PM}$.

Hence, both trains pass each other at $\mathbf{5}\mathbf{}\mathbf{PM}$.