Speed, Time and Distance
- A man walks a distance of 35 kms. He walks for some time at 4 km per hour and for some time at 5 km per hr. If he walks at 5 km per hr. instead of 4 km per hr. and 4 km per hr. instead of 5 km per hr, he will walk 2 kms more in the same span of time. Find his total time of total journey.
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Let the man walks for x hours at 4 km per hr. and y hours at 5 km per hr. and covers a distance of 35 kms.
∴ Distance = 4x + 5y = 35 ...(i)
Now, he walks at 5 km per hr.
for x hours and at 4 km per hr.
for y hours and covers a distance (35 + 2) = 37 kms
∴ Distance = 5x + 4y = 37...(ii)
By 5 × (i) – 4 × (ii) we have20x + 25y = 175 20x + 16y = 148 - - - ____________ 9y = 27
⇒ y = 3
Putting the value of (y) in equation (i), we have
4x + 5 × 3 = 35
⇒ 4x = 35 – 15 = 20
⇒ x = 5
∴ Total time taken
= x + y = 5 + 3 = 8 hours.Correct Option: C
Let the man walks for x hours at 4 km per hr. and y hours at 5 km per hr. and covers a distance of 35 kms.
∴ Distance = 4x + 5y = 35 ...(i)
Now, he walks at 5 km per hr.
for x hours and at 4 km per hr.
for y hours and covers a distance (35 + 2) = 37 kms
∴ Distance = 5x + 4y = 37...(ii)
By 5 × (i) – 4 × (ii) we have20x + 25y = 175 20x + 16y = 148 - - - ____________ 9y = 27
⇒ y = 3
Putting the value of (y) in equation (i), we have
4x + 5 × 3 = 35
⇒ 4x = 35 – 15 = 20
⇒ x = 5
∴ Total time taken
= x + y = 5 + 3 = 8 hours.
- A man travels 400 kms in 4 hours partly by air and partly by train. If he had travelled all the way by air,
and would have arrived his destination 2 hours early. Find the distance he travelled by train.he would have saved 4 of the time he was in train 5
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Obviously, 4/5 of total time in train = 2 hours
∴ Total time in train = 5 × 2 = 5 hours 4 2
Total time to cover 400 km is 4 hours
∴ Time spent in travelling by air= 4 − 5 = 8 − 5 = 3 hours 2 2 2
If 400 kms is travelled by air, then time taken = 2 hours
∴ In 2 hours, distance covered by air = 400 kmsIn 3/2 hours distance covered = 400 × 3 = 300 kms 2 2
Distance covered by the train
= 400 – 300 = 100 kms.Correct Option: D
Obviously, 4/5 of total time in train = 2 hours
∴ Total time in train = 5 × 2 = 5 hours 4 2
Total time to cover 400 km is 4 hours
∴ Time spent in travelling by air= 4 − 5 = 8 − 5 = 3 hours 2 2 2
If 400 kms is travelled by air, then time taken = 2 hours
∴ In 2 hours, distance covered by air = 400 kmsIn 3/2 hours distance covered = 400 × 3 = 300 kms 2 2
Distance covered by the train
= 400 – 300 = 100 kms.
- On increasing the speed of a train at the rate of 10 km per hr, 30 minutes is saved in a journey of 100 kms. Find the initial speed of train.
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Let the original speed be x km/hr
then, increased speed
= (x + 10) km/hr
According to question,100 − 100 = 30 x x + 10 60
[ ∵ Original time − New time= 30 minute or 30 hr ] 60 ⇒ 100 
1 − 1 
= 1 x x + 10 2 ⇒ x + 10 − x = 1 x(x + 10) 200
⇒ 10 × 200 = x (x + 10)
⇒ x2 + 10x – 2000 = 0
⇒ x2 + 50x – 40x – 2000 = 0
⇒ x (x + 50) – 40 (x + 50) = 0
⇒ x = – 50, 40
Speed can’t be negative.
Hence, Original speed = 40 kmphCorrect Option: A
Let the original speed be x km/hr
then, increased speed
= (x + 10) km/hr
According to question,100 − 100 = 30 x x + 10 60
[ ∵ Original time − New time= 30 minute or 30 hr ] 60 ⇒ 100 1 − 1 = 1 x x + 10 2 ⇒ x + 10 − x = 1 x(x + 10) 200
⇒ 10 × 200 = x (x + 10)
⇒ x2 + 10x – 2000 = 0
⇒ x2 + 50x – 40x – 2000 = 0
⇒ x (x + 50) – 40 (x + 50) = 0
⇒ x = – 50, 40
Speed can’t be negative.
Hence, Original speed = 40 kmph
- Ravi can walk a certain distance in 40 days when he rests 9 hours a day. How long will he take to walk twice the distance, twice as fast and rest twice as long each day?
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Working hours per day= 24 – 9 = 15 hrs.
Total working hours for 40 days
= 15 × 40 = 600 hrs.
On doubling the distance, the time required becomes twice but on walking twice as fast, the time required gets halved. Therefore, the two together cancel each other with respect to time required. Increasing rest to twice reduces walking hours per day to
24 – (2 × 9) = 6 hrs.
∴ Total number of days required to cover twice the distance, at twice speed with twice the rest.= 600 = 100 days 6 Correct Option: B
Working hours per day= 24 – 9 = 15 hrs.
Total working hours for 40 days
= 15 × 40 = 600 hrs.
On doubling the distance, the time required becomes twice but on walking twice as fast, the time required gets halved. Therefore, the two together cancel each other with respect to time required. Increasing rest to twice reduces walking hours per day to
24 – (2 × 9) = 6 hrs.
∴ Total number of days required to cover twice the distance, at twice speed with twice the rest.= 600 = 100 days 6
- A monkey climbing up a greased pole ascends 12 metres and slips down 5 metres in alternate minutes. If the pole is 63 metres high, how long will it take him to reach the top?
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In 1 minute the monkey climbs 12 metres but then he takes 1 minute to slip down 5
metres. So, at the end of 2 minutes the net ascending of the monkey is 12 – 5 = 7 metres.
So, to cover 63 metres the aboveprocess is repeated 63 = 9 7
times. Obviously, in 9 such happenings the monkey will slip 8 times, because on 9th time, it
will climb to the top. Thus, in climbing 8 times and slipping 8 times, he covers 8 × 7 = 56 metres.
Time taken to cover 56 metres= 56 × 2 = 16 minutes 7
Remaining distance
= 63 – 56 = 7 metres
Time taken to ascend 7 metres= 7 minutes 12 ∴ Total time taken = 16 + 7 12 = 16 7 minutes. 12 Correct Option: C
In 1 minute the monkey climbs 12 metres but then he takes 1 minute to slip down 5
metres. So, at the end of 2 minutes the net ascending of the monkey is 12 – 5 = 7 metres.
So, to cover 63 metres the aboveprocess is repeated 63 = 9 7
times. Obviously, in 9 such happenings the monkey will slip 8 times, because on 9th time, it
will climb to the top. Thus, in climbing 8 times and slipping 8 times, he covers 8 × 7 = 56 metres.
Time taken to cover 56 metres= 56 × 2 = 16 minutes 7
Remaining distance
= 63 – 56 = 7 metres
Time taken to ascend 7 metres= 7 minutes 12 ∴ Total time taken = 16 + 7 12 = 16 7 minutes. 12
