Damn two trains

Algebra Level 3

The difference between the speeds of two trains is $10\text{ km/hr}$ . The slower train begins journey from a station and when it covers $160\text{ km}$ , the faster train begins journey from the same station on a parallel line and reaches the destination $1\text{ hour}$ before the slower one. But if the faster train begins journey after covering $120\text{ km}$ by the slower one, then it can reaches the destination $2\text{ hours}$ before the slower one. What is the speed (in $\text{ km/hr}$ ) of the faster train ?

Bonus question : If you can solve it, please share it with distance between the stations!

The answer is 50.

1 solution

Chew-Seong Cheong
Nov 12, 2015

Let the distance between the station and destination be $D$ and the speed of the slower train be $v$ km/hr, therefore, that of the faster train is $v + 10$ km/hr. Then we have:

$\begin{cases} \dfrac{D-160}{v} - \dfrac{D}{v+10} = 1 & ...(1) \\ \dfrac{D-120}{v} - \dfrac{D}{v+10} = 2 & ...(2) \end{cases}$

$\begin{aligned} (2)-(1): \quad \frac{40}{v} & = 1 \\ \Rightarrow v &= 40 \text{ km/hr} \end{aligned}$

$\Rightarrow$ The speed of the faster train is $v+10 = \boxed{50}$ km/hr.

For $\color{#3D99F6}{\text{Bonus}}$ :

$\begin{aligned} (1): \quad \dfrac{D-160}{v} - \dfrac{D}{v+10} & = 1 \\ \dfrac{D-160}{40} - \dfrac{D}{40+10} & = 1 \\ \dfrac{D}{40} - 4 - \dfrac{D}{50} & = 1 \\ \dfrac{D}{200} & = 5 \\ \Rightarrow D & = \boxed{1000} \text{ km} \end{aligned}$

Damn two trains

The answer is 50.

1 solution

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