Speed, Time and Distance
- One third of a certain journey is covered at the rate of 25 km/hour, one-fourth at the rate of 30 km/hour and the rest at 50 km/hour. The average speed for the whole journey is
-
View Hint View Answer Discuss in Forum
Let the total distance be x km.
Total time = x x 5x 3 + 4 + 12 25 30 50 = x + x + x 75 120 120 = x + x 75 60 = 4x + 5x = 3x hours 300 100 ∴ Average speed = Total distance Time taken
=x 3x 100 = 100 = 33 1 kmph 3 3
Second Method :
Here, x = 3, u = 25, y = 4, v = 30z = 12 , w = 50 5 Average Speed = 1 1 + 1 + 1 xu yv zw = 1 1 + 1 + 1 3 × 25 4 × 30 (12/5) × 50 = 1 1 + 1 + 1 75 120 120 = 1 1 + 1 75 60
=1 4 + 5 300 = 300 = 100 9 3 = 33 1 km/hr. 3 Correct Option: B
Let the total distance be x km.
Total time = x x 5x 3 + 4 + 12 25 30 50 = x + x + x 75 120 120 = x + x 75 60 = 4x + 5x = 3x hours 300 100 ∴ Average speed = Total distance Time taken
=x 3x 100 = 100 = 33 1 kmph 3 3
Second Method :
Here, x = 3, u = 25, y = 4, v = 30z = 12 , w = 50 5 Average Speed = 1 1 + 1 + 1 xu yv zw = 1 1 + 1 + 1 3 × 25 4 × 30 (12/5) × 50 = 1 1 + 1 + 1 75 120 120 = 1 1 + 1 75 60
=1 4 + 5 300 = 300 = 100 9 3 = 33 1 km/hr. 3
- A man completes 30 km of a journey at the speed of 6 km/hr and the remaining 40 km of the journey in 5 hours. His average speed for the whole journey is
-
View Hint View Answer Discuss in Forum
Time taken to cover 30km at 6 kmph = 30 = 5 hours 6
Time taken to cover 40 km = 5 hours∴ Average speed = Total distance Time taken = 30 + 40 10 = 70 = 7 kmph 10 Correct Option: A
Time taken to cover 30km at 6 kmph = 30 = 5 hours 6
Time taken to cover 40 km = 5 hours∴ Average speed = Total distance Time taken = 30 + 40 10 = 70 = 7 kmph 10
- A man covers the journey from a station A to station B at a uniform speed of 36 km/hr and
returns to A with a uniform speed of 45 km/hr. His average speed for the whole journey is :
-
View Hint View Answer Discuss in Forum
Here same distances are covered at different speeds.
∴ Average speed = 
2xy 
kmph x + y = 
2 × 36 × 45 
kmph (36 + 45) = 2 × 36 × 45 = 40 kmph 81 Correct Option: A
Here same distances are covered at different speeds.
∴ Average speed = 2xy kmph x + y = 2 × 36 × 45 kmph (36 + 45) = 2 × 36 × 45 = 40 kmph 81
- P travels for 6 hours at the rate of 5 km/ hour and for 3 hours at the rate of 6 km/ hour. The average speed of the journey in km/ hour is
-
View Hint View Answer Discuss in Forum
Total distance
= 5 × 6 + 3 × 6
= 30 + 18 = 48 km
Total time = 9 hours∴ Average speed = 48 = 16 = 5 1 kmph 9 3 3 Correct Option: B
Total distance
= 5 × 6 + 3 × 6
= 30 + 18 = 48 km
Total time = 9 hours∴ Average speed = 48 = 16 = 5 1 kmph 9 3 3
- With an average speed of 40 km/hr, a train reaches its destination in time. If it goes with an average speed of 35 km/hr, it is late by 15 minutes. The total journey is
-
View Hint View Answer Discuss in Forum
Let the length of journey be x km, then
x − x = 15 = 1 35 40 60 4 ⇒ 8x − 7x = 1 280 4 ⇒ x = 280 = 70 km 4 Correct Option: C
Let the length of journey be x km, then
x − x = 15 = 1 35 40 60 4 ⇒ 8x − 7x = 1 280 4 ⇒ x = 280 = 70 km 4
