Speed, Time and Distance
- A and B run a kilometre and A wins by 25 sec. A and C run a kilometre and A wins by 275 m. When B and C run the same distance, B wins by 30 sec. The time taken by A to run a kilometre is
-
View Hint View Answer Discuss in Forum
If A covers the distance of 1 km in x seconds, B covers the distance of 1 km in (x + 25) seconds. If A covers the distance of 1 km, then in the same time C covers only 725 metres.
If B covers 1 km in (x + 25) seconds, then C covers 1 km in (x + 55) seconds.
Thus in x seconds, C covers the distance of 725 m.∴ x × 1000 = x + 55 725
⇒ x = 145
∴ A covers the distance of 1 km in 2 minutes 25 seconds.Correct Option: A
If A covers the distance of 1 km in x seconds, B covers the distance of 1 km in (x + 25) seconds. If A covers the distance of 1 km, then in the same time C covers only 725 metres.
If B covers 1 km in (x + 25) seconds, then C covers 1 km in (x + 55) seconds.
Thus in x seconds, C covers the distance of 725 m.∴ x × 1000 = x + 55 725
⇒ x = 145
∴ A covers the distance of 1 km in 2 minutes 25 seconds.
- Two cars start at the same time from one point and move along two roads at right angles to each other. Their speeds are 36 km/ hour and 48 km/hour respectively. After 15 seconds the distance between them will be
-
View Hint View Answer Discuss in Forum
Let O be the starting point. The car running at 36 kmph is moving along OB and that at 48 kmph moving along OA. Also let they reach at B and A respectively after 15 seconds.∴ OA = 48 × 5 × 15 = 200 m 18 ∴ and OB = 36 × 5 × 15 = 150 m 18
∴ Required distance = AB
= √(200)2 + (150)2
W (By Pythagoras theorem)
= √40000 + 22500
= √62500
= 250 mCorrect Option: D
Let O be the starting point. The car running at 36 kmph is moving along OB and that at 48 kmph moving along OA. Also let they reach at B and A respectively after 15 seconds.∴ OA = 48 × 5 × 15 = 200 m 18 ∴ and OB = 36 × 5 × 15 = 150 m 18
∴ Required distance = AB
= √(200)2 + (150)2
W (By Pythagoras theorem)
= √40000 + 22500
= √62500
= 250 m
- In a kilometre race, A beats B by 30 seconds and B beats C by 15 seconds. If A beats C by 180 metres, the time taken by A to run 1 kilometre is
-
View Hint View Answer Discuss in Forum
A beats B by 30 seconds and B beats C by 15 seconds.
Clearly, A beats C by 45 seconds.
Also, A beats C by 180 metres.
Hence, C covers 180 metres in 45 seconds.∴ Speed of C = 180 = 4 m/sec 45
∴ Time taken by C to cover 1000 m= 1000 = 250 sec. 4
∴ Time taken by A to cover 1000 m
= 250–45 = 205 sec.Correct Option: B
A beats B by 30 seconds and B beats C by 15 seconds.
Clearly, A beats C by 45 seconds.
Also, A beats C by 180 metres.
Hence, C covers 180 metres in 45 seconds.∴ Speed of C = 180 = 4 m/sec 45
∴ Time taken by C to cover 1000 m= 1000 = 250 sec. 4
∴ Time taken by A to cover 1000 m
= 250–45 = 205 sec.
- Ravi has a roadmap with a scale of 1.5 cm for 18 km. He drives on that road for 72 km. What would be his distance covered in that map?
-
View Hint View Answer Discuss in Forum
∵ 18 km ≡ 1.5 cm
∴ 1 km ≡ 1.5 cm 18 Correct Option: B
∵ 18 km ≡ 1.5 cm
∴ 1 km ≡ 1.5 cm 18
- Ram arrives at a Bank 15 minutes earlier than scheduled time if he drives his car at 42 km/hr. If he drives car at 35 km/hr he arrives 5 minutes late. The distance of the Bank from his starting point is
-
View Hint View Answer Discuss in Forum
Let the required distance be x km.
Difference of time = 15 + 5 = 20 minutes= 1 hour 3
According to the question,x − x = 1 ⇒ 6x − 5x = 1 35 42 3 210 3 ⇒ x = 1 210 3 ⇒ x = 210 = 70 km. 3 Correct Option: A
Let the required distance be x km.
Difference of time = 15 + 5 = 20 minutes= 1 hour 3
According to the question,x − x = 1 ⇒ 6x − 5x = 1 35 42 3 210 3 ⇒ x = 1 210 3 ⇒ x = 210 = 70 km. 3
