Question

An express train takes 1 hour less than a passenger train to travel 132km between Mysore and Bangalore. If the average speed of the express train is 11km/h more than that of the passenger train,find the average speed of the two trains

Answer 1

Answer:

12

Step-by-step explanation:

132/11

because we have take out avg speed

distance/speed

Answer 2

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☯️An express train takes 1 hour less than a passenger train to travel 132km between Mysore and Bangalore. If the average speed of the express train is 11km/h more than that of the passenger train,find the average speed of the two trains...?

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✏Avg. speed of passenger train is 33 km/hr

✏Avg. speed of express train is 44 km/hr.

$\huge{ \underline{ \bold{ \star{ \red{ \: Solution...}}}}}$

$\large{ \sf{ \diamond{ \: let \: the \: speed \: of \: passenger \: train \: be \: x}}} \\ \\ \large{ \sf{ \star{ \red{ \underline{passenger \: train}}}}} \\ \\ \large{ \sf{ \mapsto{ \: distance \: travelled = 132 \: km}}} \\ \\ \large{ \sf{ \mapsto{ speed = x}}} \\ \\ \large{ \sf{ \bullet{ \: \: speed = \frac{distance}{time \: taken} }}} \\ \\ \large{ \sf{ \mapsto{x = \frac{132}{time \: taken} }}} \\ \\ \large{ \sf{ \star{ \purple{ \: \: \: \: time \: taken = \frac{132}{x} }}}}$

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$\large{ \red{ \underline{ \sf{express \: train}}}} \\ \\ \large{ \sf{ \mapsto{distance = 132 \: km}}} \\ \\ \large{ \sf{ \bullet{ \: \: given \: that \: speed \: of \: express \: train \: is \: 11 \: more \: than \: passenger}}} \\ \\ \large{ \sf{ \mapsto{speed \: of \: express \: train = x + 11}}} \\ \\ \large{ \sf{ \green{similarly....}}} \\ \large{ \sf{ \star{ \purple{time \: taken = \frac{132}{x + 11} }}}}$

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$\large{ \bullet{ \sf{ \: \: given \: time \: taken \: by \: express \: is \: 1hr \: less \: than \: as \: passengers}}} \\ \\ \large{ \sf{ then \: \frac{132}{x} - \frac{132}{x + 11} = 1}} \\\sf{\green{\dag{\underline{(taking \:132\: as\: common)}}}}\\ \\ \large{ \sf{ \mapsto{ \frac{132(x + 11) - 132x}{x(x + 11)} = 1}}} \\ \\ \large{ \sf{ \mapsto{ \frac{132( \cancel{x} + 11 \cancel{ - x})}{ {x}^{2} + 11x } = 1}}} \\ \\ \large{ \sf{ \mapsto{ \frac{11}{ {x}^{2} + 11x} = \frac{1}{132} }}} \\ \\ \large{ \sf{ \mapsto{ {x}^{2} + 11x = 1452}}} \\ \sf{\green{\dag{\underline{(cross \:multiplied..)}}}}\\ \\ \large{ \sf{ \mapsto{ {x}^{2} + 11x - 1452 = 0}}} \\ \\ \large{ \sf{ \mapsto{ {x}^{2} + 44x - 33x - 1452 = 0}}} \\ \sf{\green{\dag{\underline{(by \:middle\: term \:factorization)}}}}\\ \\ \large{ \sf{ \mapsto{x(x + 44) - 33(x + 44) = 0}}} \\ \\ \large{ \sf{ \mapsto{(x + 44)(x - 33) = 0}}} \\ \\ \large{ \sf{ \mapsto{x = 33 \: or \: - 44}}} \\ \\ \large{ \sf{ \bullet{ \: \: since \: x \: is \: average \: speed \: it \: cant \: be \: negative.. }}} \\ \\ \large{ \sf{ \implies{ \: so \: \: x = 33}}} \\ \\ \large{ \sf{\star{ \purple{avg. \: speed \: of \: passenger \: train = 33 \: km \: h {}^{ - 1} }}}} \\ \large{ \sf{\star{ \purple{avg. \: speed \: of \: express \: train = x + 11 = 44 \: km \: h {}^{ - 1} }}}}$

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$\large{ \green{ \bold{ \underline{required \: answers \: are \: 33 \: and \: 44 \: km \: h {}^{ - 1} }}}}$