Speed, Time and Distance
 A student goes to school at the
If he travels at the speed of 3 km/hr, he reaches 10 minutes earlier. The distance of the school israte of 5 km/hr and reaches 6 minutes late. 2

 45 km
 20 km
 10 km
 4 km

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Distance of school = x km
Difference of time= 16 minutes = 16 hour 60 ∴ x − x = 16 5/2 3 60 ⇒ 2x − x = 4 5 3 15 ⇒ 6x − 5x = 4 15 15 ⇒ x = 4 15 15 ⇒ x = 4 × 15 = 4km 15
Second Method :Here, S_{1} = 5 ,t_{1} = 6 2
S_{2} = 3, t_{2} = 10Distance = (S_{1} × S_{2})(t_{1} + t_{2}) S_{1} − S_{2} = 5 × 3(6 + 10) 2 3  5 2 = 15 × 16 km = 4 km. 60 Correct Option: D
Distance of school = x km
Difference of time= 16 minutes = 16 hour 60 ∴ x − x = 16 5/2 3 60 ⇒ 2x − x = 4 5 3 15 ⇒ 6x − 5x = 4 15 15 ⇒ x = 4 15 15 ⇒ x = 4 × 15 = 4km 15
Second Method :Here, S_{1} = 5 ,t_{1} = 6 2
S_{2} = 3, t_{2} = 10Distance = (S_{1} × S_{2})(t_{1} + t_{2}) S_{1} − S_{2} = 5 × 3(6 + 10) 2 3  5 2 = 15 × 16 km = 4 km. 60
 A truck travels at 90 km/hr for
Find the time taken by the truck to travel 310 kilometres.the first 1 1 hours. After that it travels at 70 km/hr. 2

 2.5 hrs
 3 hrs
 3.5 hrs
 4 hrs

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Distance covered by truck in 3 hours 2
= Speed × Time= 90 × 3 = 135 km 2
Remaining distance
= 310 – 135 = 175 km
∴ Time taken at 70 kmph= 175 = 2.5 hours 70
∴ Total time = 1.5 + 2.5 = 4 hoursCorrect Option: D
Distance covered by truck in 3 hours 2
= Speed × Time= 90 × 3 = 135 km 2
Remaining distance
= 310 – 135 = 175 km
∴ Time taken at 70 kmph= 175 = 2.5 hours 70
∴ Total time = 1.5 + 2.5 = 4 hours
 A is twice as fast as B and B is thrice as fast as C is. The journey
covered by C in 1 1 hours will be covered by A in 2

 15 minutes
 20 minutes
 30 minutes
 1 hour

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Speed of B = x kmph (let)
Speed of A = 2x kmphSpeed of C = x kmph 3 ∴ Speed of A = 2x = 6 Speed of C (x/3) ∴ Required time = 1 of 3 hours 6 2 = 1 hour = 15 minutes 4 Correct Option: A
Speed of B = x kmph (let)
Speed of A = 2x kmphSpeed of C = x kmph 3 ∴ Speed of A = 2x = 6 Speed of C (x/3) ∴ Required time = 1 of 3 hours 6 2 = 1 hour = 15 minutes 4
 Motorcyclist P started his journey at a speed of 30 km/hr. After 30 minutes, motorcyclist Q
started from the same place but with a speed of 40 km/hr. How much time (in hours) will Q take to overtake P ?

 1

3 2 
3 8  2

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Distance covered by motor cyclist P in 30 minutes
= 30 × 1 = 15 km 2
Relative speed
= 40 – 30 = 10 kmph
∴ Required speed = Time taken to cover is km at 10 kmph= 15 = 3 hour 10 2 Correct Option: B
Distance covered by motor cyclist P in 30 minutes
= 30 × 1 = 15 km 2
Relative speed
= 40 – 30 = 10 kmph
∴ Required speed = Time taken to cover is km at 10 kmph= 15 = 3 hour 10 2
 A train covers a distance of 10 km in 12 minutes. If its speed is decreased by 5 km/hr, the time taken by it to cover the same distance is equal to

 40 minutes

40 minutes 3  20 minutes
 15 minutes

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Time = 12 minutes
= 12 hour = 1 hour 60 5 Speed of train = 10 1 5
= 50 kmph
New speed = 50 – 5 = 45 kmph∴ Required time = Distance Speed = 10 = 2 hour 45 9 = 2 × 60 minutes 9 = 40 minutes 3
Second Method :Here, S_{1} = 10 km/min 12 = 10 × 60km/hr 12 = 50 km/hr, t_{1} = 12 = 1 hr 60 5
S_{2} = 45 km/hr, t_{2} = ?
S_{1}t_{1} = S_{2}t_{2}50 × 1 = 45 × t_{2} 5 t_{2} = 10 × 60 min 45 = 40 min 3 Correct Option: B
Time = 12 minutes
= 12 hour = 1 hour 60 5 Speed of train = 10 1 5
= 50 kmph
New speed = 50 – 5 = 45 kmph∴ Required time = Distance Speed = 10 = 2 hour 45 9 = 2 × 60 minutes 9 = 40 minutes 3
Second Method :Here, S_{1} = 10 km/min 12 = 10 × 60km/hr 12 = 50 km/hr, t_{1} = 12 = 1 hr 60 5
S_{2} = 45 km/hr, t_{2} = ?
S_{1}t_{1} = S_{2}t_{2}50 × 1 = 45 × t_{2} 5 t_{2} = 10 × 60 min 45 = 40 min 3