hr more than that of the passenger train, then average speed of express train is...

Question :-

An express train takes 2 hours less than a passenger train to travel 264 km between Mysore and Bangalore. If the average speed of the express train is 22 km/hr more than that of the passenger train, then average speed of express train is : ___.

Solution :-

Let,

speed of express train = x km/h

then,

speed of passenger train = (x - 22) km/h

distance to be travelled = 264 km

using formula,

time = distance / speed

and

According to the question

$\frac{264}{x} + 2 = \frac{264}{x - 22}$

$\frac{264}{x - 22} - \frac{264}{x} = 2$

taking LCM

$\frac{264x -(x - 22)(264)}{x(x - 22)} = 2$

$\frac{264x - 264x +5808 }{ {x}^{2} - 22x } = 2$

cross multiplying

$5808 = 2 {x}^{2} - 44x$

$2 {x}^{2} - 44x - 5808 = 0$

dividing by 2 both sides

${x}^{2} - 22x - 2904 = 0$

${x}^{2} - 66x + 44x - 2904 = 0$

$x(x - 66) + 44(x - 66) = 0$

$(x + 44)(x - 66) = 0$

Form here,

x = - 44

and

x = 66

Since,

speed can't be negative

therefore

we will accept

x = 66

So,

Questions

Answers & Comments

Question :-

Solution :-

average speed of express train will be

66 km/h.

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