Question

3).A train Meerut at 6 a.m. and reaches Delhi at 10 a.m. another train leaves Delhi at 8 a.m. and reaches Meerut at 11:30 a.m. at what time do trains cross one another ?

Answer 1

Answer:

Step-by-step explanation:

Let the distance between Meerut and Delhi be y km.

Average speed of the train leaving Meerut = y/4 km/hr.

Average speed of the train leaving Delhi = 2y/7 km/hr.

suppose they meet x hrs. after 6 a.m

then, xy/4 + 2y (x-2)/7 = y

⇒ x/4 + 2x-4/7 = 1

⇒ 15x = 44

∴ x = 44/15 = 2 hrs. 56 min

So, the train meet at 8:56 a.m

Answer 2

The two trains cross each other at 8:56 a.m.

Given:

A train leaves Meerut at 6 a.m. and reaches Delhi at 10 a.m. another train leaves Delhi at 8 a.m. and reaches Meerut at 11:30 a.m.

To Find:

The time two trains cross one another.

Solution:

Let the distance between Meerut and Delhi is x km.

The time taken by the train to reach Delhi from Meerut is 4 hours.

So the speed of the train during this visit is

$\frac{x}{4}\, km/hr$

The time taken by the train to reach Meerut from Delhi is $3\frac{1}{2}\, hours=\frac{7}{2}\,hours$.

So the speed of the train during this visit is

$\frac{2x}{7}\, km/hr$

Let the trains meet at 'm' hours if the reference time taken is 6 a.m.

Then the total distance is,

$\frac{mx}{4}+\frac{2(m-2)x}{7}=x$

Cancel out 'x' from both sides of the equation.

$\frac{m}{4}+\frac{2(m-2)}{7}=1$

The LCM of 4 and 7 is 28. Use the LCM and solve the equation for 'm'.

$\frac{7m}{28}+\frac{8(m-2)}{28}=1\\7m+8m-16=28\\15m=44\\m=2\, hours\, 56\, minutes$

The value of 'm' came out to be 2 hours 56 minutes which means that there is a gap of 2 hours 56 minutes between 6 a.m and the time at which the two trains met. So, the trains met at 8:56 a.m.

Thus, the two trains cross each other at 8:56 a.m.

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