## Speed, Time and Distance

#### Speed, Time and Distance

1.  A man covers 2 of the total journey 15
 by train, 9 by bus and the remaining 20
10 km on foot. His total journey (in km) is
1. 15.6
2. 24
3. 16.4
4. 12.8

1. Let the total journey be of x km, then

 2x + 9x + 10 = x 15 20

 ⇒  x − 2x − 9x = 10 15 20

 ⇒ 60x − 8x − 27x = 10 60

 ⇒ 25x = 10 60

 ⇒ x = 60 × 10 = 24 km 25

##### Correct Option: B

Let the total journey be of x km, then

 2x + 9x + 10 = x 15 20

 ⇒  x − 2x − 9x = 10 15 20

 ⇒ 60x − 8x − 27x = 10 60

 ⇒ 25x = 10 60

 ⇒ x = 60 × 10 = 24 km 25

1. A speed of 30.6 km/.hr is the same as
1. 8.5 m/sec.
2. l0 m/sec.
3. 12 m/sec.
4. 15.5 m/sec.

1. 30.6 kmph

 30.06 × 5 m/sec. 18

= 8.5 m/sec

##### Correct Option: A

30.6 kmph

 30.06 × 5 m/sec. 18

= 8.5 m/sec

1. A man rides at the rate of 18 km/ hr, but stops for 6 mins. to change horses at the end of every 7th km. The time that he will take to cover a distance of 90 km is
1. 6 hrs.
2. 6 hrs. 12 min.
3. 6 hrs. 18 min.
4. 6 hrs. 24 min.

1. 90 km = 12 × 7km + 6 km. To

 cover 7 km total time taken = 7 8

 hours + 6 min. = 88 min. So, 3

(12 × 7 km) would be covered in
 12 × 88 min. and remaining 6 km is 6 hrs or 20 min 3 18

 ∴  Total time = 1056 + 20 3

 = 1116 hours = 6 1 hours 3 × 60 5

= 6 hours 12 minutes.

##### Correct Option: B

90 km = 12 × 7km + 6 km. To

 cover 7 km total time taken = 7 8

 hours + 6 min. = 88 min. So, 3

(12 × 7 km) would be covered in
 12 × 88 min. and remaining 6 km is 6 hrs or 20 min 3 18

 ∴  Total time = 1056 + 20 3

 = 1116 hours = 6 1 hours 3 × 60 5

= 6 hours 12 minutes.

1. A train covers a certain distance in 210 minutes at a speed of 60 kmph. The time taken by the train, to cover the same distance at a speed of 80 kmph is :
1.  3 5 hours 8
2.  2 5 hours 8
3.  4 5 hours 8
4. 3 hours

1. Speed of train = 60 kmph
Time = 210 minutes

 = 210 hours 60

 or 7 hours 2

 Distance covered = 60 × 7 = 210 km 2

 Time taken at 80 kmph = 210 = 21 hours 80 8

 = 2 5 hours 8

Second Method :
 Here, S1 60, t1 = 210 hrs 60

S2 = 80, t2 = ?
S1t1 = S2t2
 60 × 210 = 80 × t2 60

 t2 = 2 5 hrs 8

##### Correct Option: B

Speed of train = 60 kmph
Time = 210 minutes

 = 210 hours 60

 or 7 hours 2

 Distance covered = 60 × 7 = 210 km 2

 Time taken at 80 kmph = 210 = 21 hours 80 8

 = 2 5 hours 8

Second Method :
 Here, S1 60, t1 = 210 hrs 60

S2 = 80, t2 = ?
S1t1 = S2t2
 60 × 210 = 80 × t2 60

 t2 = 2 5 hrs 8

1.  The speed 3 1 m/sec when expressed 3
in km/hour becomes
1. 8
2. 9
3. 10
4. 12

1.  ∵  1 m/sec = 18 kmph 5

 ∴ 10 m/sec 3

 = 18 × 10 = 12 kmph 5 3

##### Correct Option: D

 ∵  1 m/sec = 18 kmph 5

 ∴ 10 m/sec 3

 = 18 × 10 = 12 kmph 5 3