Question

1. Question 6.
A train started at 8 a.m. from station A with a speed of 60 km/hr. After 2 hours, another train started from station B towards A with a speed of 72 km/hr. The two trains are expected to cross each other at 12.30 p.m. Owing to
signal problems arising at 11 a.m., the speed of each of them was reduced by the same quantity and they crossed each other at 3p.m. What is the new speed of the train that started from station A?​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

New speed of the train that started from station A is 18.75 km/hr

Given:

• Train started at 8 a.m. from station A with a speed of 60 km/hr.
• After 2 hours, another train started from station B towards A with a speed of 72 km/hr.
• The two trains are expected to cross each other at 12.30 p.m.
• Signal problems arised at 11 a.m
• the speed of each of them was reduced by the same quantity
• Trains crossed each other at 3p.m.

To Find:

• New speed of the train that started from station A?​

Solution:

Distance = Speed x Time

Step 1:

Find Distance to be covered by Train from Station A.

Time = 12 : 30 - 8  = 4 .5 hrs

Speed = 60 km/hr

Distance = 60 x 4.5 = 270 km

Step 2:

Find Distance to be covered by Train from Station B.

Time =  4 .5 - 2 = 2.5 hrs

Speed = 72 km/hr

Distance = 72 x 2.5 = 180 km

Step 3:

Find  Total Distance to be covered

270 + 180 = 450 km

Step 4:

Find  Total Distance  covered till 11 AM      

(11 - 8 = 3  and 3 - 2 = 1)

60 x 3  + 72 x 1  

= 180 + 72

= 252 km

Step 5:

Find remaining Distance

450 - 252  = 198 km

198 km distance was to be covered in 1.5 hrs   ( 12 : 30 - 11: 00)

But covered in 4 hrs  ( 3 PM - 11 AM)

Total Speed was (60 + 72) = 132 km/hr

Verified 198/132 = 1.5 hrs

New Total Speed = 198/4  = 49.5 km/hr

Step 6:

Assume that Speed of each train reduced by x km/hr

Speed of Trains  60 - x  and 72 - x

Then Total New speed = 132 - 2x  

Step 7:

Equate total new speed with 49.5 and solve for x

 132 - 2x   = 49.5  

=> x = 41.25

Step 8:

Calculate 60 - x by substituting  x = 41.25

60 - x = 60 - 41.25

= 18.75

Hence  New speed of the train that started from station A is 18.75 km/hr