Question

Train x takes 30 minutes more than train y to cover 36 km if due to some reason speed of train y becomes one fourth than that of previous then it takes 15 minutes more than train x to cover the same distance find the difference in speed of train x and y ?

Answer 1

Given:

Train x takes 30 minutes more than train y to cover 36 km

Due to some reason speed of train y becomes one fourth than that of previous then it takes 15 minutes more than train x to cover the same distance

To find:

The difference in speed of train x and y

Solution:

Let' s assume,

"X" km/hr → be the speed of train x

"Y" km/hr → be the speed of train y

We have, train x takes 30 minutes more than train y to cover a distance of 36 km, so by using the formula $Time = \frac{Distance}{Speed}$ we can form an eq. as,

$\frac{36}{X} \:-\: \frac{36}{Y} \:=\:\frac{30}{60}$

⇒ $\frac{36}{X} \:-\: \frac{36}{Y} \:=\:\frac{1}{2}$

⇒ $\frac{1}{X} \:-\: \frac{1}{Y} \:=\:\frac{1}{72}$

⇒ $\frac{1}{X} \:=\:\frac{1}{72} \:+\: \frac{1}{Y} \:$ ....... (i)

Also,

Speed of train y becomes 1/4th of the previous speed i.e., now the speed becomes $\frac{Y}{4}$, because of which train y takes  15 minutes more than train x to cover the same distance.

∴ $\frac{36}{\frac{Y}{4}} \:-\: \frac{36}{X} \:=\:\frac{15}{60}$

⇒ $\frac{36}{\frac{Y}{4}} \:-\: \frac{36}{X} \:=\:\frac{1}{4}$

⇒ $\frac{144}{Y} \:-\: \frac{36}{X} \:=\:\frac{1}{4}$

⇒ $36[\frac{4}{Y} \:-\: \frac{1}{X} ]\:=\:\frac{1}{4}$

⇒ $[\frac{4}{Y} \:-\: \frac{1}{X} ]\:=\:\frac{1}{144}$

substituting from (i)

⇒ $\frac{4}{Y} \:-[\frac{1}{72} \:+\: \frac{1}{Y} ]\:=\:\frac{1}{144}$

⇒ $\frac{4}{Y} \:-\frac{1}{72} \:-\: \frac{1}{Y} \:=\:\frac{1}{144}$

⇒ $\frac{4}{Y} \:-\: \frac{1}{Y} \:=\:\frac{1}{144}\:+\frac{1}{72}$

⇒ $\frac{4 - 1}{Y}\:=\:\frac{1+ 2}{144}$

⇒ $\frac{3}{Y}\:=\:\frac{3}{144}$

⇒ $\bold{Y = 144 \:km/hr}$

Now, by substituting Y = 144 km/hr in eq. (i), we get

$\frac{1}{X} \:=\:\frac{1}{72} \:+\: \frac{1}{144} \:$

⇒ $\frac{1}{X} \:=\:\frac{2+1}{144}$

⇒ $\frac{1}{X} \:=\:\frac{3}{144}$

⇒ $X \:=\:\frac{144}{3}$

⇒ $\bold{X \:=\:48\:km/hr}$

∴ The difference in speed of train x and y = X - Y = 144 - 48 = 96 km/hr

Thus, the difference in speed of train x and y is 96 km/hr.

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