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# Abdul travelled 300 km by train and 200 km by taxi, it took him 5 hours 30 minutes. But it he travels 260 km by train and 240 km by taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi.

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This question is taken from linear equations in two variables in which we have to find the speed of the train and the taxi if a person took 5 hrs 30 mins travel a distance of 300 km by train and 200 km by taxi and it took longer time if it travels 260 km by train and 240 km by taxi.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3E, question no 33

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1. ## Let, the speed of train =x km/h and the speed of the taxi =y km/h.

Now using  time=distance​/speed, we get,
300/x + 200/y=11​/2     ………..(1) and
260/x + 240/y = 5+ 36/60 = 5+ 3/5=28/5     ……….(2)
Let, x1 =m and y1 =n then,
600m+400n=11    ……….(3)
1300m+1200n=28    ………(4)

Now, equation (3)×3 equation (4)×4 we get,

500m=5
m=1/100
x=100 km/h.
Putting the value of m in equation (3) we get,
n=5/400=1/80
y=80 km/h.
Speed of train =100 km/h.
Speed of taxi =80 km/h.

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