## Speed, Time and Distance

#### Speed, Time and Distance

1.  Walking at 6 th of his usual speed a man 7
is 25 minutes late. His usual time to cover this distance is
1. 2 hours 30 minutes
2. 2 hours 15 minutes
3. 2 hours 25 minutes
4. 2 hours 10 minutes

1. Time and speed are inversely proportional.

 ∴ 7 × Usual time – Usual time = 25 minutes 6

 ⇒ 7 − 1 = 25 minutes 6

 ⇒  Usual time × 1 = 25 minutes 6

∴  Usual time = 25 × 6
= 150 minutes
= 2 hours 30 minutes
Second Method :
Here, A = 6, B = 7,
 t = 25 = 5 hrs. 60 12

 Usual time = A × time Diff. of A and B

 = 6 × 5 = 5 hrs. (7 − 6) 12 2

= 2 hours 30 minutes

##### Correct Option: A

Time and speed are inversely proportional.

 ∴ 7 × Usual time – Usual time = 25 minutes 6

 ⇒ 7 − 1 = 25 minutes 6

 ⇒  Usual time × 1 = 25 minutes 6

∴  Usual time = 25 × 6
= 150 minutes
= 2 hours 30 minutes
Second Method :
Here, A = 6, B = 7,
 t = 25 = 5 hrs. 60 12

 Usual time = A × time Diff. of A and B

 = 6 × 5 = 5 hrs. (7 − 6) 12 2

= 2 hours 30 minutes

1.  Walking at 3 of his usual speed, 4
 a man is 1 1 hours late. His usual time to 2
cover the same distance, (in hours) is
1.  4 1 2
2. 4
3.  5 1 2
4. 5

1. Time and speed are inversely proportional.

 ∴ 4 of usual time –usual time 3

 = 3 2

 ⇒ 1 × usual time = 3 3 2

 ∴  Usual time = 3 × 3 = 9 2 2

 = 4 1 hours 2

Second Method :
 Here, A = 3, B = 4, t = 3 2

 Usual time = A × time Diff. of A and B

 = 3 × 3 (4 − 3) 2

 = 4 1 hrs. 2

##### Correct Option: A

Time and speed are inversely proportional.

 ∴ 4 of usual time –usual time 3

 = 3 2

 ⇒ 1 × usual time = 3 3 2

 ∴  Usual time = 3 × 3 = 9 2 2

 = 4 1 hours 2

Second Method :
 Here, A = 3, B = 4, t = 3 2

 Usual time = A × time Diff. of A and B

 = 3 × 3 (4 − 3) 2

 = 4 1 hrs. 2

1.  By walking at 3 of his usual speed, 4
a man reaches his office 20 minutes later than his usual time. The usual time taken by him to reach his office is
1. 75 minutes
2. 60 minutes
3. 40 minutes
4. 30 minutes

1.  4 of usual time = Usual time + 20 minutes 3

 ∴ 1 of usual time = 20 minutes 3

⇒  Usual time = 20 × 3
= 60 minutes
Second Method :
Here, A = 3, B= 4, t = 20 minutes
 Usual time taken = A × time Diff. of A and B

 = 3 × 20 = 60 minutes (4 − 3)

##### Correct Option: B

 4 of usual time = Usual time + 20 minutes 3

 ∴ 1 of usual time = 20 minutes 3

⇒  Usual time = 20 × 3
= 60 minutes
Second Method :
Here, A = 3, B= 4, t = 20 minutes
 Usual time taken = A × time Diff. of A and B

 = 3 × 20 = 60 minutes (4 − 3)

1. Walking at three-fourth of his usual speed, a man covers a certain distance in 2 hours more than the time he takes to cover the distance at his usual speed. The time taken by him to cover the distance with his usual speed is
1. 4.5 hours
2. 5.5 hours
3. 6 hours
4. 5 hours

1.  4 ×usual time – usual time = 2 3

 ⇒ 1 usual time = 2 3

∴  Usual time = 2 × 3 = 6 hours
Second Method :
 Here, A = 3 , time= 2 hrs. B 4

 Usual time= A × time Diff. of A and B

 = 3 × 2 = 6 hours (4 − 3)

##### Correct Option: C

 4 ×usual time – usual time = 2 3

 ⇒ 1 usual time = 2 3

∴  Usual time = 2 × 3 = 6 hours
Second Method :
 Here, A = 3 , time= 2 hrs. B 4

 Usual time= A × time Diff. of A and B

 = 3 × 2 = 6 hours (4 − 3)

1.  A car travelling with 5 of its usual speed covers 7
42 km in 1 hour 40 min 48 sec. What is the usual speed of the car?
1.  17 6 km/hr 7
2. 35 km/hr
3. 25 km/hr
4. 30 km/hr

1. 1 hr 40 min 48 sec

 = 1 hr 40 + 48 min 60

 = 1 hr 40 + 4 min 5

 = 1 hr 204 min 5

 = 1 + 204 hr 300

 = 504 hr 300

 ∴  Speed = 42 504 300

= 25 kmph
 Now, 5 ×usual speed = 25 7

 ∴  Usual speed = 25 × 7 5

= 35 kmph

##### Correct Option: B

1 hr 40 min 48 sec

 = 1 hr 40 + 48 min 60

 = 1 hr 40 + 4 min 5

 = 1 hr 204 min 5

 = 1 + 204 hr 300

 = 504 hr 300

 ∴  Speed = 42 504 300

= 25 kmph
 Now, 5 ×usual speed = 25 7

 ∴  Usual speed = 25 × 7 5

= 35 kmph