Question

The distance between Vijayawada and Gudur is 293 km. Howrah to Tirupathi train T1
passes Vijayawada at 8 AM and reaches Gudur at 1400 hr. ‘Tirupathi-Hyderabad express
T2 crosses Gudur at 7.45 Am and reaches Vijayawada by 13.30 hr.(assuming no stops),
at what time do they cross each other?

Answer 1

They meet at 2.45 pm.

Step-by-step explanation:

Since we have given that

Distance between Vijayawada and Gudur = 293 km

Howrah to Tirupathi train T1  passes Vijayawada at 8 AM and reaches Gudur at 1400 hr.

Time = 6 hours

Tirupathi-Hyderabad express

T2 crosses Gudur at 7.45 Am and reaches Vijayawada by 13.30 hr.

Time = $5\dfrac{45}{60}\\\\=5\dfrac{3}{4}\\\\=\dfrac{23}{4}$

Distance = l.c.m. of 6 and $\dfrac{23}{4}$=138 km

So, Speed of T1 = $\dfrac{138}{6}=23\ km/hr$

Speed of T2 = $138\div \dfrac{23}{4}=138\times \dfrac{4}{23}=24\ km/hr$

So, relative speed = 24+23=47 km/hr as they move in opposite direction.

Distance covered between 7:45 pm to 8:00 = $\dfracf{138}{6}\times \dfrac{15}{60}=5.75\ km$

Distance left = 293-5.75=287.25 km

So,time they cross each other is given by

$\dfrac{287.25}{47}=6.11\ hours\approx 6\ hours$

They meet at 2.45 pm.