Speed, Time and Distance
- A student goes to his school from his house walking at 4 km/h and reaches his school 10 min late. Next day, starting at the same time he walks as 6 km/h and reaches his school 5 min earlier than the scheduled time. Find the distance between school and home ?
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Let the distance be x km.
∴ Time = Distance/speed
1st day time taken = x/4 h
2nd day time taken = x/6 h
Difference in time = (x/4 - x/6) h
Actual difference between these two times = 15 min = 1/4 h
∴ x/4 - x/6 = 1/4 ⇒ (3x - 2x)/12 = 1/4Correct Option: B
Let the distance be x km.
∴ Time = Distance/speed
1st day time taken = x/4 h
2nd day time taken = x/6 h
Difference in time = (x/4 - x/6) h
Actual difference between these two times = 15 min = 1/4 h
∴ x/4 - x/6 = 1/4 ⇒ (3x - 2x)/12 = 1/4
∴ x = 3 km
- Two train of length 250 m and 140 m are running on parallel lines in the same direction at 58 km/h and 32 km/h, respectively. Find the time taken by the slower train to pass the driver of the faster one ?
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Relative speed = (58 - 32) = 26 km/h
= 26 x (5/18) m/s = 65/9 m/s
Time taken to cross each other = (250 + 140)/(65/9)
Correct Option: B
Relative speed = (58 - 32) = 26 km/h
= (26 x 5/18) m/s = 65/9 m/s
Time taken to cross each other = (250 + 140)/(65/9)
= (390 x 9)/65 = 54 s
- A person travelled a distance of 50 km in 8 h. He covered a part of the distance on foot at the rate of 4 km/h and a part on a bicycle at the rate of 10 km/h. How much distance did he travel on foot ?
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Let T h, he travels on foot.
∴ 4T + 10(8 - T) = 50Correct Option: B
Let T h, he travels on foot.
∴ 4T + 10(8 - T) = 50
⇒ 80 - 6T = 50
⇒ 6T = 30,
∴ T = 5 h
∴ The distance travelled on foot = 4 x 5 = 20 km
- 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
- 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