## Speed, Time and Distance

#### Speed, Time and Distance

1. For every 4 leaps taken by a dog, a cat takes 5 leaps in the same time. But distance covered in 3 leaps of dog is same as that of 4 leaps of cat. Then what is the ratio of speed of dog and cat ?
1. 15 : 14
2. 16 :15
3. 12 :11
4. 10 : 9

1. Ratio of speed of dog and cat = Ratio of distance covered by them in the same time

##### Correct Option: B

Let distance covered by dog in 1 leap is x and
Distance covered by cat in 1 leap is y

Then, 3x = 4y
∴ x= 4/3y

Now, Ratio of speed of dog and cat = Ratio of distance covered by them in the same time = 4x : 5y
= 16/3y : 5y
= 16 : 15

1. Suresh traveled 1200 km by air which formed (2/5) of his trip. One-third of the whole trip he traveled by car And the rest of the journey he performed by train. The distance traveled by train was ?
1. 1600 km.
2. 800 km.
3. 1800 km.
4. 400 km.

1. Let the total distance be y km.
Then, 2y / 5 = 1200
⇒ y = (1200 x 5) /2 = 3000 km.

Distance traveled by car
= (1/3 X 3000) = 1000 km.

##### Correct Option: B

Let the total distance be y km.
Then, 2y / 5 = 1200
⇒ y = (1200 x 5) /2 = 3000 km.

Distance traveled by car
= (1/3 X 3000) = 1000 km.

Distance traveled by train
= [3000- (1200 + 1000) ] km.
= 800 km.

1. Two cyclists A and B start from the same place at the same time. One going toward north at 18 km/hr. and other going toward south at 20 km/hr. What time will they take to be 95 km. apart ?
1. 4 hrs. 30 min.
2. 4 hrs. 45 min.
3. 5 hrs.16 min.
4. 2hrs. 30 min

1. Relative velocity = u + v = 18 + 20 = 38 km
They are 38 km. apart in 1 hr.

##### Correct Option: D

Relative velocity = u + v = 18 + 20 = 38 km
They are 38 km. apart in 1 hr.
∴ They will be 95 km. apart in ( 95 / 38) hrs.
= 2 hrs . 30 min

1. A bullock cart has to cover a distance of 80 km. in 10 hours. If it cover half of journey in 3/5th time, what should be its speed to cover the remaining distance in time left ?
1. 8 km/hr.
2. 20 km/hr.
3. 6.4 km/hr.
4. 10 km/hr.

1. Distance left = (1/2 x 80 ) km. = 40km.
Time left - [(1-3/5) x 10 ] hrs.
= 4 hours

##### Correct Option: D

Distance left = (1/2 x 80 ) km. = 40km.
Time left - [(1-3/5) x 10 ] hrs.
= 4 hours

Required speed = (40 / 4 ) km/hr
= 10 km/hr.

1. The ratio between the rates of travelling of A and B is 2:3 and therefore A takes 10 min. more than the time taken by B to reach a destination, if A had walked at double the speed, he would have covered the distance in ?
1. 30 min
2. 25 min
3. 15 min
4. 20 Min

1. Ratio of times taken by A and B = 1/2 : 1/3

Suppose B takes Tb min. Then A takes (Tb + 10) min.
∴ (Tb + 10 ) : Tb = 1/2: 1/3
⇒ (Tb + 10)/Tb = 3 / 2
⇒ 2Tb + 20 = 3Tb
∴ Tb = 20

##### Correct Option: C

Ratio of times taken by A and B = 1/2 : 1/3

Suppose B takes Tb min. Then A takes (Tb + 10) min.
∴ (Tb + 10 ) : Tb = 1/2: 1/3
⇒ (Tb + 10)/Tb = 3 / 2
⇒ 2Tb + 20 = 3Tb
∴ Tb = 20

∴ Time taken by A = 20 +10
= 30 minute

If A had walked at double speed
Req . time = 30/2
=15 minute