Worksheet Solutions: Idea of Speed, Distance and Time | Mathematics Class 6 ICSE PDF Download

A. Multiple Choice Questions 

Q1. A scooter covers 27 km in 45 minutes. What is its speed in km/h?
(a) 18 km/h
(b) 27 km/h
(c) 36 km/h
(d) 45 km/h
Ans: (c) 36 km/h

Sol: 
45 min = 45/60 = 0.75 h. 
Speed = Distance ÷ Time 
= 27 ÷ 0.75 
= 36 km/h.

Q2. Convert 36 km/h to m/s.
(a) 8 m/s
(b) 10 m/s
(c) 12 m/s
(d) 18 m/s
Ans: (b) 10 m/s
Sol: To change km/h to m/s, multiply by 5/18. 
So, 36 × 5/18 
= 10 m/s.

Q3. Which is the correct unit of speed when distance is in metres and time in seconds?
(a) cm/min
(b) km/h
(c) m/s
(d) m/min
Ans: (c) m/s
Sol: Speed unit = (unit of distance)/(unit of time). 
With metres and seconds → m/s.

Q4. Two walkers move in opposite directions from the same point at 4 km/h and 6 km/h. What is the distance between them after 2 hours?
(a) 10 km
(b) 12 km
(c) 18 km
(d) 20 km
Ans: (d) 20 km
Sol: Relative speed (opposite) = 4 + 6 = 10 km/h. 
Distance = 10 × 2 = 20 km.

Q5. A car’s speed is 54 km/h. Which option shows the same speed in m/s?
(a) 12 m/s
(b) 13.5 m/s
(c) 15 m/s
(d) 18 m/s
Ans: (c) 15 m/s
Sol: 54 km/h → 54 × 5/18 
= 15 m/s.

B) Short Answer Questions 

Q6. A car moves at 32 km/h for 45 minutes. Find the distance covered (in km).

Ans: 
45 min = 0.75 h. 
Distance = Speed × Time 
= 32 × 0.75 
= 24 km.

Q7. A cyclist covers 18 km at 12 km/h. Find the time taken in hours and minutes.
Ans: 
Time = Distance ÷ Speed 
= 18 ÷ 12 
= 1.5 h 
= 1 h 30 min.

Q8. Convert 10 m/s to km/h.
Ans: 
 To change m/s to km/h, 
multiply by 18/5. 
So, 10 × 18/5 = 36 km/h.

Q9. A runner’s speed is 5 m/s. How much distance does the runner cover in 2 minutes 30 seconds?
Ans: 
2 min 30 s = 150 s. 
Distance = Speed × Time 
= 5 × 150 = 750 m.

Q10. A bus covers 14.4 km in 30 minutes. Find its speed in km/h.
Ans: 
30 min = 0.5 h. 
Speed = 14.4 ÷ 0.5 
= 28.8 km/h.

C) Long Answer Questions

Q11. An athlete runs 360 m in 45 s.
(a) Find the speed in m/s.
(b) How much distance will the athlete cover in 12 s at the same speed?
(c) How much time will the athlete take to cover 0.5 km?

Sol:
(a) Speed = Distance ÷ Time 
= 360 ÷ 45 
= 8 m/s
(b) Distance = Speed × Time 
= 8 × 12 
= 96 m
(c) 0.5 km = 500 m. 
Time = Distance ÷ Speed 
= 500 ÷ 8 
= 62.5 s

Q12. A traveller goes 60 km at 30 km/h, then 90 km at 60 km/h.
(a) Find the total time taken.
(b) Find the average speed for the whole journey.

Ans:
Time₁ = 60 ÷ 30 = 2 hours
Time₂ = 90 ÷ 60 = 1.5 hours
Total time = 2 + 1.5 = 3.5 hours
Total distance = 60 + 90 = 150 km
Average speed = Total distance ÷ Total time
= 150 ÷ 3.5
= 1500 ÷ 35
= 300 ÷ 7 km/h
≈ 42.86 km/h
$\frac{300}{7}km/h\approx 42.86km/h$

Q13. A train of length 180 m runs at 72 km/h. Find the time to pass
(a) a pole, and
(b) a platform of length 270 m.

Sol:
Convert speed: 72 km/h 
= 72 × 5/18 
= 20 m/s

(a) Past a pole: Distance = train length = 180 m.
Time = Distance ÷ Speed 
= 180 ÷ 20 
= 9 s

(b) Past a platform: Distance = train + platform 
= 180 + 270 
= 450 m
Time = 450 ÷ 20 = 22.5 s