A car travels 80 km in 2 hours and a train travels 180 km in 3 hours. What is the ratio of the speed of the car to the speed of the train?

Introduction / Context:
This is a basic speed, distance and time question that asks for the ratio of two speeds. Each speed can be computed using the formula speed = distance / time. Then we form the ratio of the car speed to the train speed and simplify it. Such questions test fundamental understanding of motion and proportional reasoning.

Given Data / Assumptions:

• Car travels 80 km in 2 hours.
• Train travels 180 km in 3 hours.
• We assume both move at constant speed over the given distances.
• We are required to find (speed of car) : (speed of train).

Concept / Approach:
Speed is defined as distance divided by time. Once we compute each speed numerically, we express the two speeds as a ratio and then reduce that ratio to its simplest form by dividing both parts by their greatest common divisor. This uses straightforward arithmetic and is a direct application of the definition of speed.

Step-by-Step Solution:
Speed of car = distance / time = 80 km / 2 hours. So speed of car = 40 km per hour. Speed of train = 180 km / 3 hours. So speed of train = 60 km per hour. Required ratio = speed of car : speed of train = 40 : 60. Divide both sides by 20 to simplify: 40 / 20 = 2 and 60 / 20 = 3. Hence the ratio is 2 : 3.

Verification / Alternative check:
We can check using proportional thinking. Car covers 80 km in 2 hours, so in 3 hours at the same speed it would cover 120 km. Train covers 180 km in 3 hours, which is clearly faster. The ratio 120 : 180 also simplifies to 2 : 3, consistent with the earlier calculation. This confirms that our ratio is correct.

Why Other Options Are Wrong:
3 : 2 or 4 : 3 would suggest the car is faster than the train, which is not the case because 40 km per hour is less than 60 km per hour. Ratios like 3 : 4 or 5 : 4 do not match the true speed ratio when the distances and times are checked.

Common Pitfalls:
A common mistake is to compare distances directly (80 and 180) without adjusting for the different times, or to compare times without considering distances. Another error is to forget to simplify the ratio after calculating the speeds. Always compute speed first using distance over time, then form and simplify the ratio to get the final answer.

Final Answer:
The ratio of the speed of the car to the speed of the train is 2 : 3.