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# trains

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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 ?

Feb 9, 2021

#1
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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

Feb 9, 2021