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 ?
+128474 Let the speed of the slower train = R
Let the rate of the faster train = R + 10
Let the whole distance = D
Then in the first situation :
The time it takes the faster train to cover the whole distance plus 1 hour =
The time it takes the slower train to cover the whole distance - 160 km
And in the second situation :
The time it takes the faster train to cover the whole distance plus 2 hours =
The time it takes the slower train to cover the whole distance - 160 km
So we have this system
D / (R +10) - 1 = ( D - 160) / R
D / (R + 10) - 2 = (D -120) / R
Solving this for D , R we get that
D = 1000km
R = 40 km/hr
R + 10 = 50 km/hr = the rate of the faster train
