Question

hey everyone.. i am going through great difficulty. please me out. so the question goes like this
Abdul travel 300 km by train and 200 km by taxi, it took him 5 hours 30 minutes. but if he travels 260 km by train and 240 by bus he takes 6 minutes longer. find the speed of the train and of the taxi.

Answer 1

hii dear,
here is your answer,

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Let the speed of train and taxi be x km/hr and y km/hr respectively.

Now,

time taken by train to cover 300 km = 300/x hours

and time taken by taxi to cover 200 km = 200/3 hours

also

total time taken = 5 hours 30 minutes

$5 \frac{1}{2} \: hours = \frac{11}{2} hours \\ = > \frac{300}{x} + \frac{200}{y} = \frac{11}{2 } \\ = \frac{600}{x} + \frac{400}{y} = 11 \: - - - (1)$




also time taken by train to cover 260 km = 260/x hours

time taken by taxi to cover 240 km = 240/y hours

and total time taken = 5 hours 30 minutes + 6 minutes

= 5 hours 36 minutes 
$= 5 \frac{5}{3} hours$
$= \frac{28}{5} hours \\ = > \frac{260}{x} + \frac{240}{y} = \frac{28}{5} \\ = \: \frac{325}{x } + \frac{300}{y} = 7 \: - - - (2)$


Putting 1/x = u and 1/y = v in (1) and (2) we get

600 u + 400 v = 11 ... (3)

325 u + 300 v = 7 ... (4)

Solving (3) and (4)

$u = \frac{1}{100} \: and \: v = \frac{1}{80}$


⇒ x = 100 and y = 80

Hence the speed of the train is 100 km/hr

and the speed of the taxi is 80 km/hr

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Hope it helps u !!!

Cheers ☺☺