⏱️ SPEED, DISTANCE & TIME MASTERCLASS
[Image of formula triangle for speed distance time]
Basic Formula: Speed = Distance ÷ Time
Conversion: km/hr × 5/18 = m/sec
Average Speed: Total Distance ÷ Total Time
Relative Speed: Same direction (Subtract) | Opposite (Add)
1️⃣ Question
A person walks 750 meters in 6 minutes. What is their speed in kilometers per hour?
✏️ Solution
Distance = 750 m = 0.75 km
Time = 6 min = 6/60 = 0.1 hours
Speed = 0.75 ÷ 0.1 = 7.5 km/h
✅ Correct Answer: B) 7.5
2️⃣ Question
A vehicle travels a fixed distance at 180 km/h in 6 hours. At what speed must it travel to cover the same distance in 2.5 hours?
✏️ Solution
Step 1: Find Distance = Speed × Time = 180 × 6 = 1080 km
Step 2: New Speed = Distance ÷ New Time
Speed = 1080 ÷ 2.5 = 432 km/h
✅ Correct Answer: C) 432 km/h
3️⃣ Question
If someone cycles at 18 km/h instead of 12 km/h, they would cover 24 km more in the same time period. What is the actual distance they cycled?
✏️ Solution
Let time = t hours.
Distance difference = (18 × t) - (12 × t) = 24
6t = 24 → t = 4 hours.
Actual Distance (at 12 km/h) = 12 × 4 = 48 km.
✅ Correct Answer: A) 48 km
4️⃣ Question
A high-speed train is 50% faster than a car. Both travel 90 km from City X to City Y. The train loses 15 minutes at stops but they arrive simultaneously. What is the car's speed?
✏️ Solution
Car Speed = v. Train Speed = 1.5v (50% faster).
Time difference due to speed = Stop time = 15 min (0.25 hr).
90/v - 90/1.5v = 0.25
90/v (1 - 2/3) = 0.25 → 90/v (1/3) = 0.25
30/v = 0.25 → v = 120 km/h.
✅ Correct Answer: D) 120 km/h
5️⃣ Question
Without stops, a bus travels at 48 km/h. With stops included, its effective speed is 40 km/h. How many minutes does it stop per hour?
✏️ Solution
Formula: Stop Time = (Difference in Speed ÷ Original Speed) × 60
Diff = 48 - 40 = 8.
Time = (8 ÷ 48) × 60 = (1/6) × 60 = 10 minutes.
✅ Correct Answer: B) 10
6️⃣ Question
A 720 km airplane trip had speed reduced by 180 km/h due to headwinds, increasing travel time by 40 minutes (2/3 hrs). What was the original travel duration?
✏️ Solution
Let original time = t. Original Speed = 720/t.
Using quadratic equation for time/speed, we find:
Original Speed = 540 km/h. Reduced Speed = 360 km/h.
Original Time = 720 ÷ 540 = 1.33 hours (1 hr 20 min).
Note: Closest option is 1.5 hours, but mathematically it is 1 hr 20 min.
✅ Best Answer: A) 1.5 hours
7️⃣ Question
A journey takes 10 hours. The first half is at 18 km/h, the second half at 27 km/h. What is the total journey length?
✏️ Solution
Average Speed = (2 × 18 × 27) ÷ (18 + 27) = 972 ÷ 45 = 21.6 km/h.
Total Distance = Avg Speed × Time
Distance = 21.6 × 10 = 216 km.
✅ Correct Answer: A) 216 km
8️⃣ Question
Two vehicles have speed ratio 3:4. The faster covers 360 km in 3 hours. What is the slower vehicle's speed?
✏️ Solution
Faster speed = 360 ÷ 3 = 120 km/h.
Ratio = 3 : 4.
4 parts = 120, so 1 part = 30.
Slower speed (3 parts) = 3 × 30 = 90 km/h.
✅ Correct Answer: C) 90 km/h
9️⃣ Question
First 200 km at 50 km/h, next 200 km at 80 km/h. What's the average speed for 400 km?
✏️ Solution
Time 1 = 200 ÷ 50 = 4 hours.
Time 2 = 200 ÷ 80 = 2.5 hours.
Total Time = 6.5 hours. Total Dist = 400 km.
Avg Speed = 400 ÷ 6.5 ≈ 61.5 km/h.
✅ Correct Answer: A) 61.5 km/h
🔟 Question
At 3/4 of normal speed, a car covers 36 km in 1 hour 30 minutes. What is its normal speed?
✏️ Solution
Current Speed = 36 ÷ 1.5 = 24 km/h.
3/4 of Normal = 24
Normal = 24 × (4/3) = 32 km/h.
✅ Correct Answer: C) 32 km/h
1️⃣1️⃣ Question
To cover 36 km, Alex takes 3 hours more than Ben. If Alex doubles speed, he takes 1.5 hours less than Ben. What is Alex's original speed?
✏️ Solution
Total gap in Alex's time = 3 - (-1.5) = 4.5 hours.
Let Alex speed = v. Time gap between speed v and 2v is 4.5h.
36/v - 36/2v = 4.5
36/v (1 - 0.5) = 4.5 → 18/v = 4.5
v = 4 km/h.
✅ Correct Answer: A) 4 km/h
1️⃣2️⃣ Question
Maya will arrive at 3 PM cycling at 8 km/h. At 12 km/h she'd arrive at 1 PM. What speed gets her there at 2 PM?
✏️ Solution
Difference in time = 2 hours.
Distance/8 - Distance/12 = 2 → Distance = 48 km.
Time at 8km/h = 48/8 = 6 hrs (Arrive 3 PM → Start 9 AM).
Target: Arrive 2 PM (5 hours travel time).
Speed = 48 ÷ 5 = 9.6 km/h.
✅ Correct Answer: B) 9.6 km/h
1️⃣3️⃣ Question
500 km trip takes 10 hours if 100 km by train, rest by car. Takes 30 minutes more if 150 km by train, rest by car. Train to car speed ratio?
✏️ Solution
Replacing 50km Car with 50km Train adds 30 mins.
Calculated ratio is 9:14.
Closest approximate option is 3:4.
✅ Best Answer: B) 3:4
1️⃣4️⃣ Question
Traveler goes 76 km in 10 hours, partly walking at 5 km/h, partly biking at 10 km/h. Walking distance?
✏️ Solution
Let walk time = w. Bike time = 10-w.
5w + 10(10-w) = 76
5w + 100 - 10w = 76 → 24 = 5w → w = 4.8 hours.
Walk distance = 5 × 4.8 = 24 km.
✅ Correct Answer: D) 24 km
1️⃣5️⃣ Question
A fixed distance is covered at constant speed. If speed increases 4 km/h, time decreases 45 minutes. If speed decreases 3 km/h, time increases 45 minutes. What is the distance?
✏️ Solution
Using simultaneous equations for Time and Speed changes.
Speed calculated = 24 km/h. Distance = 126 km.
Note: The options provided do not match the mathematical result for these specific numbers (likely a variation of a standard exam question).
✅ Correct Answer: 126 km (Calculation)
