Question

A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/hr more. Find the original speed of the train.​

Answer 1

Six months ago, the worst thing that ever happened to me was the biggest news on the internet. Now.

Six months ago, the worst thing that ever happened to me was the biggest news on the internet. Now.The Universe is thought to consist of three types of substance: normal matter, 'dark matter' and 'dark energy

Answer 2

let original speed of train = x km/h

we know,

$\huge \mathsf{ \color{purple}{time = \frac{distance}{speed} }}$

first case

———————

$\ \mathsf{ \color{pink}{time \: taken \: by \: train \: = \frac{360}{x} \: hour }}$

second case

——————————

$\small \mathsf{ \color{green}{time \: taken \: by \: train \: its \: speed \: increase \: \frac{5 km}{h} = \frac{360}{( x + 5)} }}$

question says that

time taken by train in first - time taken by train in 2nd case = 48 min = 48/60 hour

$360/x - 360/(x +5) = 48/60 = 4/5$

$360{ 1/x - 1/(x +5) } = 4/5$

$360 ×5/4 { 5/(x² +5x )} =1$

$450 x 5 = x² + 5x$

$x² +5x -2250 = 0$

x = { -5±√(25+9000) }/2

=(-5 ±√(9025) )/2

=(-5 ± 95)/2

= -50 , 45

but x ≠ -50 because speed doesn't negative

so, x = 45 km/h

$\small \mathsf{ \color{blue}{ hence, \: original \: speed \: of \: train \: = \frac{45 km}{h} }}$