A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.
Answers
SOLUTION :
Given: Total distance of a journey = 200 km
Let the speed of the slow train be x km/h and the speed of the fast train is (x + 10) km)h.
Time taken by the slow train to cover 200 km= 200/x hrs
Time taken by the fast train to cover 200 km= 200/(x +10) hrs
[ Time = Distance/speed]
200/(x +10) = 200/ x - 1
200/ x - 200/(x +10) = 1
[200(x + 10) - 200x] /(x(x + 10) = 1
[By taking LCM]
200x + 2000 - 200x /(x(x+10) = 1
2000 / x² + 10x = 1
(x² +10x ) = 2000
x² + 10x - 2000 = 0
x² + 50x - 40x -2000 = 0
[By middle term splitting]
x(x + 50) - 40 ( x + 50) = 0
(x - 40) (x + 50) = 0
x = 40 or x = - 50
Since, speed can't be negative, so x = - 50
Therefore, speed of the slow train be = x = 40 km/h
speed of the fast train be = (x + 10)= 40 + 10 = 50 km/h
Hence the speeds of two trains are 40 km/h and 50 km/h.
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Then, the speed of the slow train be = (x-10) km/hr
Time taken by the fast train to cover 200 km = 200/x hr
Time taken by the slow train to cover 200 km = 200/(x – 10) hr
200x–200(x−10)=1
(200(x–10)–200x)x(x−10)=1
200x–2000–200xx2–10x=1
x2 – 10x = – 2000
x2 – 10x + 2000 = 0
x2 – 50x + 40x + 2000 = 0
x(x – 50) + 40(x – 50) = 0
(x – 50)(x + 40) = 0
x = 50 or x = – 40
Since, the speed of train can never be negative.
Therefore, x = 50
So, speed of the fast train is 50 km/hr
And speed of slow train
(50 – 10) = 40 km/hr (given speed of slow train is 10km/hr less than fast train)
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