Question

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

Answer 1

Step-by-step explanation:

Question :-

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

Answer :-

Given :

• Train x takes 30 minutes more than train y to cover 36km
• Speed of train y become one fourth than that of previous
• It takes 15 min more than train than train x to cover the same distance

To find :

• Difference in speed of train x and train y

Solution :

Let's take speed of train y be 4y km/hr

We know that,

${\bold{\sf{Time \: = \: \frac{Distance}{Speed}}}}$

${\bold{\sf{⟼ \: \: \: \: \: Time \: taken \: by \: train \: y \: = \: \frac{36}{4y}}}}$

${\bold{\sf{⟼ \: \: \: \: \: Time \: taken \: by \: train \: y \: = \: \: \frac{9}{y}}}}$

According to question,

Train x takes 30 minutes more than train y

${\bold{\sf{⟼ \: \: \: \: \: \: Time \: taken \: by \: train \: x \: = \: \: \frac{9}{y} + \frac{1}{2}}}}$

Speed of train y reduced by 1/4

${\bold{\sf{\frac{1}{4} \: of \: 4 y \: = \: y}}}$

Now speed of train = 4y - y = 3y km/hr

${\bold{\sf{⟼ \: \: \: \: \: Time \: taken \: = \: \frac{36}{3y}}}}$

${\bold{\sf{⟼ \: \: \: \: \: Time \: taken \: = \: \frac{12}{y}}}}$

Train x takes 15 minutes more = 1/4 hr

${\bold{\sf{⟼ \: \: \: \: \: Time \: taken \: by \: train \: x \: = \: \frac{12}{y} \: + \: \frac{1}{4}}}}$

Time taken by train x

${\bold{\sf{⟼ \: \: \: \: \: \frac{9}{y} \: + \: \frac{1}{2} \: = \: \frac{12}{y} \: + \: \frac{1}{4}}}}$

Multiplying by 4y sides on both sides

${\bold{\sf{⟼ \: \: \: \: \: 36 \: + \: 2y \: = \: 48 \: + \: y}}}$

${\bold{\sf{⟼ \: \: \: \: \: y \: = \: 12}}}$

Speed of train y = 4y = 48 km/hr

${\bold{\sf{Time \: taken \: by \: train \: x \: = \: \frac{12}{y} + \frac{1}{4}}}}$

Speed of train x = 28.8 km/hr