Speed, Time and Distance
- Amit start from a point A and walks to another point B and then return from B to A by his car and thus takes a total time of 6 h 45 min. If he had driven both ways in his car, he would have taken 2 h less. How long would it take for him to walk both ways ?
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Let w be the time taken in one way by walking and c be the time taken in one way by car.
Now, according to the question,
In first case, w + c = 6 h 45 min
or
2w + 2c = 13 h 30 min ..(i)
In second case, 2c = 4 h 45 min ....(ii)
From Eqs. (i) and (ii), we get
2w + 2c = 13 h 30 min
Correct Option: D
Let w be the time taken in one way by walking and c be the time taken in one way by car.
Now, according to the question,
In first case, w + c = 6 h 45 min
or
2w + 2c = 13 h 30 min ..(i)
In second case, 2c = 4 h 45 min ....(ii)
From Eqs. (i) and (ii), we get
2w + 2c = 13 h 30 min
⇒ 2w + 4h 45 min = 13 h 30 min
⇒ 2w = 13 h 30 min - 4 h 45 min
⇒ 2w = 8 h 45 min
∴ If he walks both ways, then time taken = 8 h 45 min
- Total time taken by a person in going to a place by walking and returning on cycle is 5 h 45 min. He would have gained 2 h by cycling both ways. The time taken by him to walk both ways, is ?
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Walking time + Cycling time = 5 h 45 min = 345 min ....(i)
If he had cycled both way he would have gained 2 h (120 min).
∴ 2 x Cycling time = 345 - 120 = 225 min ...(ii)
Walking time = 2 x 345 - 225 = 690 - 225 = 465 minCorrect Option: B
Walking time + Cycling time = 5 h 45 min = 345 min ....(i)
If he had cycled both way he would have gained 2 h (120 min).
∴ 2 x Cycling time = 345 - 120 = 225 min ...(ii)
Walking time = 2 x 345 - 225 = 690 - 225 = 465 min
Time taken by him to walk both ways = 7 h 45 min
- An express train travelled at an average speed of 100 km/h, stopping for 3 min after every 75 km. A local train travelled at a speed of 50 km/h, stopping for 1 min after every 25 km. If the trains began travelling at the same time, how many kilometres did the local train travel in the time in which the express train travel 600 km ?
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Time taken by express train to cover 75 km including stoppage
= (60 / 100 x 75) min + = 48 min
Time taken by express train to cover 600 km.
= Time taken by it to cover 75 km
= (48 / 75 x 525 ) min + (60 / 100 x 75 ) min
= (336 + 45) min = 381
Time taken by local train to9 cover 25 km including stoppage
= (60 / 50 x 25) min + 1 min = 31 min
In 31 min, distance covered = 25 km
In(31 x 12) min. distance covered
= (25 / 31 x 31 x 12 ) = 300 km
In last 9 min, distance covered
Correct Option: C
Time taken by express train to cover 75 km including stoppage
= (60 / 100 x 75) min + = 48 min
Time taken by express train to cover 600 km.
= Time taken by it to cover 75 km
= (48 / 75 x 525 ) min + (60 / 100 x 75 ) min
= (336 + 45) min = 381
Time taken by local train to9 cover 25 km including stoppage
= (60 / 50 x 25) min + 1 min = 31 min
In 31 min, distance covered = 25 km
In(31 x 12) min. distance covered
= (25 / 31 x 31 x 12 ) = 300 km
In last 9 min, distance covered
= (25 / 31 x 9 ) = 7.25 km
∴ Required total distance
= 300 + 7.25 = 307.25 km
- Two cars A and B are running towards each other from two different place 88 km apart. If the ratio of the speeds of the cars A and B is 5:6 and the speeds of the cars B is 90 km/h, after what time will they meet each other ?
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Let speed of A = 5x
Then, spend of B = 6x
Given that,speed of B = 6x = 90
∴ x = 90/6 = 15
∴ Speed of A = 5x = 5x = 5 x 15 = 75 km/h
Let A and B meet after T h. Then,
75 x T + 90 x T =88Correct Option: D
Let speed of A = 5x
Then, spend of B = 6x
Given that,speed of B = 6x = 90
∴ x = 90/6 = 15
∴ Speed of A = 5x = 5x = 5 x 15 = 75 km/h
Let A and B meet after T h. Then,
75 x T + 90 x T =88
∴ T = 88/165 h = (88 x 60)/165 = 32 min
- A car starts running with the initial speed of 40 km/h with its speed increasing every hour by 5 km/h. How many hours will it taken to cover a distance of 385 km ?
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Required number of hours is the number of terms of the series 40 + 45 + 50 +... as speed increases every hour.
Given, sum of the series is 385
∴ a = 40, d=5, s = 385 and n= ?
Using S = n/2[2a + (n - 1)d]
⇒ 385 = n/2[80 + 5n - 5]Correct Option: D
Required number of hours is the number of terms of the series 40 + 45 + 50 +... as speed increases every hour.
Given, sum of the series is 385
∴ a = 40, d=5, s = 385 and n= ?
Using S = n/2[2a + (n - 1)d]
⇒ 385 = n/2[80 + 5n - 5]
⇒ 770 = 5n2 + 75n
⇒ n2 + 15n - 154 = 0
⇒ n2 + 22n - 7n - 154 = 0
⇒ n(n + 22) - 7(n + 22) = 0
⇒ (n + 22) (n - 7) = 0
∴ n = 7
Remaining part = 1/12 - 1/20 = (5 - 3)/60 = 2/60 = 1/30 i.e., 1/30 th part is filled by B in 1 min
Hence, required time to fill the whole tank = (165 + 1 + 1) min = 167 min
