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ICSE Class 10 Answered

Two trains leave a railway station at the same time .The first train travels due west and the second train due north. The first train travels 5km/hr faster than the second train. If after 2 hours, they are 50 km apart, find the speed of each train.
Asked by yashi24jan | 04 Dec, 2021, 09:42: PM
Expert Answer
Let the speed of 2nd train = x km/hr
So, speed of 1st train = (x + 5) km/hr
Distance travelled in 2 hrs
1st train = 2(x + 5)
2nd train = 2x
now they are moving perpendicular to each other and are 50km apart
Using pythagoras theorem, we have
4x2 +4(x+5)2 =502  
4x2  +4x2  +40x+100=2500
8x2  +40x−2400=0
x2  +5x−300=0
(x−15)(x+20)=0
x=15,−20
speed of 2nd train =15  km/hr
So, speed of 1st train = 20 km/hr
Answered by Arun | 06 Dec, 2021, 10:15: AM

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