Train A takes 1 hour more than Train B to travel a distance of 720 km. Later, due to engine trouble, the speed of Train B decreases by one third, so that it now takes 3 hours more than Train A to cover the same 720 km. What is the speed (in km/h) of Train A?

Introduction / Context:
This is an algebra based time, speed, and distance question set in the context of trains. Train A and Train B initially cover the same long distance with a 1 hour difference in their travel times. Later the speed of Train B is reduced, changing the time relationship. We use these conditions to determine the original speed of Train A.

Given Data / Assumptions:

• Distance for each journey = 720 km.
• Train A takes 1 hour more than Train B initially.
• Speed of Train B later becomes two thirds of its original speed.
• With reduced speed, Train B now takes 3 hours more than Train A to travel 720 km.
• Both trains travel at constant speeds during each scenario.

Concept / Approach:
Let vA and vB be the original speeds of Train A and Train B. Time is distance divided by speed. We set up one equation for the initial situation and another for the situation after Train B speed changes. This leads to two equations in the two unknowns vA and vB, which we solve simultaneously. Finally, we report the value of vA, the speed of Train A.

Step-by-Step Solution:
Step 1: Let vA be speed of Train A and vB be speed of Train B in km/h. Step 2: Initial times are tA = 720 / vA and tB = 720 / vB. Step 3: Train A takes 1 hour more, so 720 / vA = 720 / vB + 1. Step 4: After engine trouble, speed of Train B becomes (2 / 3) * vB. Step 5: New time for Train B is tB2 = 720 / ((2 / 3) * vB) = 1080 / vB. Step 6: Now Train B takes 3 hours more than Train A, so 1080 / vB = 720 / vA + 3. Step 7: Solve the system of equations: 720 / vA = 720 / vB + 1 1080 / vB = 720 / vA + 3. Step 8: Solving gives vA = 80 km/h and vB = 90 km/h.

Verification / Alternative check:
Check initial times: tA = 720 / 80 = 9 hours and tB = 720 / 90 = 8 hours, so Train A takes 1 hour more. After engine trouble, Train B speed is (2 / 3) * 90 = 60 km/h, so tB2 = 720 / 60 = 12 hours. Now tB2 - tA = 12 - 9 = 3 hours, which matches the problem statement. This confirms the result.

Why Other Options Are Wrong:

• 90 km/h: This is actually the speed of Train B, not Train A.
• 60 km/h: This is Train B speed after the engine trouble, not the original speed of Train A.
• 70 km/h: Using this value for Train A does not satisfy both time conditions simultaneously.

Common Pitfalls:
Learners may misinterpret the phrase speed falls by a third and incorrectly use vB / 3 instead of two thirds of vB. Another common mistake is mixing up which train is slower in each scenario and setting up the time differences incorrectly. It is important to carefully define variables and write each condition as a separate equation before solving.

Final Answer:
The speed of Train A is 80 km/h.