How to Solve: CUET Quant – Speed, Distance, Time, Trains, Boats and Streams

How to Solve: CUET Quant – Speed, Distance, Time, Trains, Boats and Streams

Introduction

"If you can solve a train crossing a bridge in under 30 seconds, you’ll ace 5+ questions in CUET Quant—saving time for tougher problems. Let’s break it down."

What You Need To Know First

1. Basic algebra – Rearranging equations (e.g., Speed = Distance / Time).
2. Unit conversion – km/h to m/s (multiply by 5/18), and vice versa.
3. Relative speed – When two objects move toward/away from each other.

Key Vocabulary

Formulas To Know

Step-by-Step Method

Step 1: Read the Question Carefully

• Underline what is given (speed, distance, time, lengths).
• Circle what is asked (e.g., "time taken," "speed of the boat").

Step 2: Convert Units (If Needed)

• km/h → m/s: Multiply by 5/18.
• m/s → km/h: Multiply by 18/5.
• Ensure all units match (e.g., don’t mix km and meters).

Step 3: Identify the Type of Problem

• Basic SDT? → Use D = S × T.
• Two moving objects? → Use relative speed.
• Train crossing a platform/pole? → Add lengths.
• Boat in a stream? → Use downstream/upstream speed.

Step 4: Apply the Correct Formula

• Write the formula based on the problem type.
• Plug in the given values.

Step 5: Solve for the Unknown

• Rearrange the formula if needed.
• Calculate step-by-step (show working).

Step 6: Check Units & Reasonableness

• Does the answer make sense? (e.g., speed can’t be negative).
• Are units correct? (e.g., km/h, not m/s).

Step 7: Write the Final Answer

• Box the answer.
• Include units.

Worked Example (Using Steps Above)

Question: A train 200 m long crosses a pole in 10 seconds. What is its speed in km/h?

Step 1: Given: Train length = 200 m, Time = 10 s. Asked: Speed in km/h. Step 2: Units are in meters and seconds → keep as is for now. Step 3: Train crossing a pole → Use Speed = Length / Time. Step 4: Speed = 200 m / 10 s = 20 m/s. Step 5: Convert to km/h → 20 × (18/5) = 72 km/h. Step 6: 72 km/h is reasonable for a train. Step 7: Answer: 72 km/h.

Worked Examples

Example 1 – Basic (Speed, Distance, Time)

Question: A car travels 150 km in 3 hours. What is its speed?

Solution: 1. Given: D = 150 km, T = 3 h. 2. Formula: Speed = Distance / Time. 3. S = 150 / 3 = 50 km/h. Answer: 50 km/h.

What we did and why: - Direct application of S = D / T. - No unit conversion needed.

Example 2 – Medium (Relative Speed – Trains)

Question: Two trains, 150 m and 200 m long, move toward each other at 30 km/h and 40 km/h. How long do they take to cross each other?

Solution: 1. Convert speeds to m/s:
- 30 km/h = 30 × (5/18) = 25/3 m/s.
- 40 km/h = 40 × (5/18) = 100/9 m/s. 2. Relative speed (opposite direction) = 25/3 + 100/9 = 175/9 m/s. 3. Total distance = 150 + 200 = 350 m. 4. Time = Distance / Speed = 350 / (175/9) = 350 × 9 / 175 = 18 s. Answer: 18 seconds.

What we did and why: - Used relative speed for objects moving toward each other. - Added lengths of both trains (total distance to cover).

Example 3 – Exam Style (Boats and Streams)

Question: A boat’s speed in still water is 15 km/h. The stream speed is 3 km/h. How much time will it take to go 90 km downstream?

Solution: 1. Downstream speed = Boat speed + Stream speed = 15 + 3 = 18 km/h. 2. Distance = 90 km. 3. Time = Distance / Speed = 90 / 18 = 5 hours. Answer: 5 hours.

What we did and why: - Recognized downstream = faster speed. - Applied T = D / S directly.

Common Mistakes

Exam Traps

1-Minute Recap

"Alright, last-minute review for Speed, Distance, Time in CUET Quant. Here’s what you must remember:

1. Basic formula: Speed = Distance / Time. Rearrange it—D = S × T, T = D / S.
2. Trains: If crossing a pole, use Train Length / Speed. If crossing a platform, add platform length.
3. Relative speed: Same direction? Subtract speeds. Opposite direction? Add speeds.
4. Boats: Downstream = Boat + Stream. Upstream = Boat – Stream.
5. Units: km/h to m/s? Multiply by 5/18. m/s to km/h? Multiply by 18/5.

Common traps? Forgetting to add lengths, mixing units, or misapplying relative speed. Double-check the question—are they moving toward or away? Is it downstream or upstream?

You’ve got this. Now go solve those 5 questions in under 2 minutes each!

Final Note for Teachers: - Pacing: Spend 30% of time on basics (S = D / T), 50% on relative speed/trains, 20% on boats. - Visuals: Draw trains/boats on a whiteboard for relative speed problems. - Practice: Assign 3 problems per type (basic, trains, boats) in timed conditions.