A train running between two stations arrives at it's destination 10 minutes late when it travels at 40km/hr and 16 minutes late when it travels at 30km/hr. The distance between the two stations is ?
If the distance between the stations is $\displaystyle x$ km then the time of the journey at $\displaystyle 40$ km/hr is $\displaystyle x/40$ hr, and at $\displaystyle 30$ km/hr is $\displaystyle x/30$ hr.
So:
$\displaystyle \frac{x}{30} - \frac{x}{40} = \frac{1}{10}$
(that is the difference in journey times at the two speeds is $\displaystyle 6$ minutes or $\displaystyle 1/10$ of an hour).
CB
Hello, saberteeth!
A train running between two stations arrives at its destination
10 minutes late when it travels at 40 km/hr
and 16 minutes late when it travels at 30 km/hr.
Find the distance between the two stations.
Let $\displaystyle D$ = distance (in kilometers).
Let $\displaystyle t$ = time for a normal run (in hours).
We will use: .$\displaystyle \text{Distance} \:=\: \text{Speed} \times \text{Time} \quad\Rightarrow\quad T \:=\:\frac{D}{S}$
At 40 kph, it is 10 minutes $\displaystyle \left(\tfrac{1}{6}\text{ hr}\right)$ late.
. . $\displaystyle \frac{D}{40} \:=\:t + \frac{1}{6} \quad\Rightarrow\quad D \:=\:40t + \frac{20}{3}\quad [1]$
At 30 kph, it is 16 minutes $\displaystyle \left(\tfrac{4}{15}\text{ hr}\right)$ late.
. . $\displaystyle \frac{D}{30} \:=\:t + \frac{4}{15} \quad\Rightarrow\quad D \:=\:30t + 8\quad[2]$
Equate [1] and [2]: .$\displaystyle 40t + \frac{20}{3} \:=\:30t + 8$
Hence: .$\displaystyle 10t \:=\:\frac{4}{3} \quad\Rightarrow\quad t \:=\:\frac{2}{15} $
Substitute into [1]: .$\displaystyle D \:=\:40\left(\frac{2}{15}\right) + \frac{20}{3}$
Therefore: .$\displaystyle D \:=\:12\text{ km} $
But Captain Black has an elegant solution!