Speed, Time and Distance
- A train meets with an accident after travelling 30 kms, after which it moves
at the destination 45 minutes late. Had the accident happened 18 kms further on, it would have been 9 minutes before. Find the distance of journey and original speed of the train.with 4 th of its original speed and arrives 5
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Let the original speed be x and distance be y
Case I.
Time taken by train to travel30 km = 30 x Time taken by train after accident = y − 30 4/5x Total time taken = 30 + y − 30 x 4/5x
Case II :
Time taken by train to travel48 km = 48 x Time taken by train after accident = y − 48 4/5x Total time taken = 48 + y − 48 x 4/5x 
30 + y − 30 
− 48 + y − 48 x 4/5x x 4/5x = 9 [∵ Difference between time is 9 minutes] 60 y − 30 − y − 48 + 30 − 48 4/5x 4/5x x x = 9 60 y − y − 30 + 48 + (− 18) = 9 4/5x x 60 5(18) − 18 = 9 4x 4x 60 ⇒ 90 − 72 = 9 4x 60 x = 18 × 60 = 30 4 × 9
Hence, original speed = 30 kmph
Also,30 + y − 30 = y + 45 x 4/5x x 60
[Original time + 45 minute = New time]
⇒ 3x – y = –30
⇒ 3(30) – y = –30
⇒ i.e. Distance = 120 kmCorrect Option: D
Let the original speed be x and distance be y
Case I.
Time taken by train to travel30 km = 30 x Time taken by train after accident = y − 30 4/5x Total time taken = 30 + y − 30 x 4/5x
Case II :
Time taken by train to travel48 km = 48 x Time taken by train after accident = y − 48 4/5x Total time taken = 48 + y − 48 x 4/5x 30 + y − 30 − 48 + y − 48 x 4/5x x 4/5x = 9 [∵ Difference between time is 9 minutes] 60 y − 30 − y − 48 + 30 − 48 4/5x 4/5x x x = 9 60 y − y − 30 + 48 + (− 18) = 9 4/5x x 60 5(18) − 18 = 9 4x 4x 60 ⇒ 90 − 72 = 9 4x 60 x = 18 × 60 = 30 4 × 9
Hence, original speed = 30 kmph
Also,30 + y − 30 = y + 45 x 4/5x x 60
[Original time + 45 minute = New time]
⇒ 3x – y = –30
⇒ 3(30) – y = –30
⇒ i.e. Distance = 120 km
- A train met with an accident 3 hours after starting, which detains it for one hour, after which it proceeds at 75% of its original speed. It arrives at the destination 4 hours late. Had the accident taken place 150 km further along the railway line,
Find the length of the trip and the original speed of the train.the train would have arrived only 3 1 hours late. 2
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Let A be the starting point, B the terminus. C and D are points where accidents take place.
∴ 0.75 = 3 4
By travelling a 3/4 of its original speed, the train would take 4/3 of its usual time i.e., 1/3 more of the usual time.
∴ 1/3 of the usual time taken to travel the distance CB.
= 4 – 1 = 3 hrs. ...(i)
and 1/3 of the usual time taken to travel the distanceDB = 3 1 − 1 = 2 1 hrs. ...(ii) 2 2
Subtracting equation (ii) from (i)
we can write,
1/3 of the usual time taken to travel the distanceCD = 3 − 2 1 = 1 hr. 2 2
∴ Usual time taken to travelCD (150 km) = 1 2 1 3 = 3 hr. 2
Usual speed of the train= 3 = 9 hrs. 1 3
Total time = 3 + 9 = 12 hrs.
∴ Length of the trip = 12 × 100 = 1200 km.Correct Option: B
Let A be the starting point, B the terminus. C and D are points where accidents take place.
∴ 0.75 = 3 4
By travelling a 3/4 of its original speed, the train would take 4/3 of its usual time i.e., 1/3 more of the usual time.
∴ 1/3 of the usual time taken to travel the distance CB.
= 4 – 1 = 3 hrs. ...(i)
and 1/3 of the usual time taken to travel the distanceDB = 3 1 − 1 = 2 1 hrs. ...(ii) 2 2
Subtracting equation (ii) from (i)
we can write,
1/3 of the usual time taken to travel the distanceCD = 3 − 2 1 = 1 hr. 2 2
∴ Usual time taken to travelCD (150 km) = 1 2 1 3 = 3 hr. 2
Usual speed of the train= 3 = 9 hrs. 1 3
Total time = 3 + 9 = 12 hrs.
∴ Length of the trip = 12 × 100 = 1200 km.
- Two trains A and B travel from points X to Y and the ratio of the speeds of A to that of B is 2 : 7. Find the ratio of time taken by A and B to reach From X to Y.
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We know that speed is inversely proportional to time.
Given that, (Speed of A ) : (speed of B ) = 2 : 7Correct Option: D
We know that speed is inversely proportional to time.
Given that, (Speed of A ) : (speed of B ) = 2 : 7
∴(Time taken by A ) : (Time taken by B ) = 1/2 : 1/7 = 7 : 2
- Two trains A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 km per hr. Another train starts from B at 8 am. and travels towards A at a speed of 25 km per hr. At what time will they meet?
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Let they meet x hrs after 7 am.
Distance covered by A in x hours = 20x km
Distance covered by B in (x –1) hr.
= 25 (x – 1) km
∴ 20x + 25 (x – 1) = 110
⇒ 20x + 25x – 25 = 110
⇒ 45x = 110 + 25 = 135
⇒ x = 3
∴ Trains meet at 10 a.m.Correct Option: D
Let they meet x hrs after 7 am.
Distance covered by A in x hours = 20x km
Distance covered by B in (x –1) hr.
= 25 (x – 1) km
∴ 20x + 25 (x – 1) = 110
⇒ 20x + 25x – 25 = 110
⇒ 45x = 110 + 25 = 135
⇒ x = 3
∴ Trains meet at 10 a.m.
- Two boys begin together to write out a booklet containing 817 lines. The first boy starts with the first line, writing at the rate of 200 lines an hour and the second boy starts with the last lines then writes line 816 and so on. Backward proceeding at the rate of 150 lines an hour. At what line will they meet?
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Writing ratio = 200 : 150 = 4 : 3
In a given time first boy will be writing the line number4 × 817 7 = 3268 th line = 466 6 th line 7 7
or, 467 th line
Hence, both of them shall meet on 467th line.Correct Option: A
Writing ratio = 200 : 150 = 4 : 3
In a given time first boy will be writing the line number4 × 817 7 = 3268 th line = 466 6 th line 7 7
or, 467 th line
Hence, both of them shall meet on 467th line.
