Question

A car travels \(105\) km in \(3\) hours and a train travels \(252\) km in \(4\) hours. The ratio of speed of the car to that of the train is:

• A. \(9:11\)
• B. \(3:5\)
• C. \(2:7\)
• D. \(5:9\)

Hint:

Remember: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] For ratios:

• First calculate individual speeds
• Simplify the ratio to lowest terms

Answer 1

The Correct Option is D

Concept: Speed is defined as: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] To find the ratio of speeds: \[ \text{Ratio} = \frac{\text{Speed of car}}{\text{Speed of train}} \]

Step 1: Calculate the speed of the car. Given: \[ \text{Distance} = 105\,\text{km} \] \[ \text{Time} = 3\,\text{hours} \] Using: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] \[ \text{Speed of car} = \frac{105}{3} \] \[ = 35\,\text{km/h} \]

Step 2: Calculate the speed of the train. Given: \[ \text{Distance} = 252\,\text{km} \] \[ \text{Time} = 4\,\text{hours} \] \[ \text{Speed of train} = \frac{252}{4} \] \[ = 63\,\text{km/h} \]

Step 3: Find the ratio of their speeds. \[ 35 : 63 \] Divide both terms by \(7\): \[ 5 : 9 \] Therefore, \[ \boxed{5:9} \]