Question

A train leaves Boston and travels toward its destination at a speed of $60\mathrm{mph}$. One hour later, an express train leaves Boston and travels toward the same destination at a speed of $80\mathrm{mph}$. How far away is Boston is their destination if they arrive at the same time.

Answer 1

Step-1: Relative speed of trains:

The formula for the distance is $\mathrm{distance}=\mathrm{speed}\times \mathrm{time}$.

A train leaves Boston and travels toward its destination at a speed of $60\mathrm{mph}$.

After one hour, an express train leaves Boston and travels toward the same destination at a speed of $80\mathrm{mph}$.

The difference between the speeds of the two trains will be,

$80-60=20\mathrm{mph}$

Since the express train leaves, the regular train has a $60\mathrm{miles}$ lead, which is getting shorter hour by hour because the express train travels $20\mathrm{mph}$ more than the normal train. it follows that,

Step-2: Find the time of their destination:

Let time taken by express train is $xhrs.$

$\begin{array}{rcl}\text{T}\mathrm{ime}& =& \frac{\mathrm{distance}}{\mathrm{speed}}\end{array}$

$$\begin{gathered} \text{Distance=80x=60(x+1)} \\ \Rightarrow 20x=60 \\ \Rightarrow x=3\text{hr} \end{gathered}$$

Step-3: Find the distance of their destination:

In $3\mathrm{h}$ the express train would catch up with the regular train.

Substitute $\mathrm{speed}=80\mathrm{mph}$and $\mathrm{time}=3\mathrm{h}$.

$\begin{array}{rcl}\mathrm{distance}& =& \mathrm{speed}\times \mathrm{time}\\ & \Rightarrow & \mathrm{distance}=80\times 3\\ & \Rightarrow & \mathrm{distance}=240\mathrm{miles}\end{array}$

Therefore, the required distance is $\mathbf{240}\mathbf{}\mathbf{miles}$.