Speed, Time and Distance
 A bus moving at 40 km per hour covers a distance in 6 hours 15 minutes. If it travels the same distance at 50 km per hour how long will it take to cover the distance ?

 2 hrs.
 6 hrs.
 4 hrs.
 5 hrs.

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Distance = Speed × TIme
= 40 × 6 1 km 4 = 40 × 25 km = 250 km 4
New speed = 50 kmph
∴ Required time= Distance = 250 = 5 hours Speed 50
Second Method :Here, S_{1} = 40, t_{1} = 6 15 = 25 60 4
S_{2} = 50, t_{2} = ?
S_{1}t_{1} = S_{2}t_{2}40 × 25 = 50 × t_{2} 4
t_{2} = 5 hrs.Correct Option: D
Distance = Speed × TIme
= 40 × 6 1 km 4 = 40 × 25 km = 250 km 4
New speed = 50 kmph
∴ Required time= Distance = 250 = 5 hours Speed 50
Second Method :Here, S_{1} = 40, t_{1} = 6 15 = 25 60 4
S_{2} = 50, t_{2} = ?
S_{1}t_{1} = S_{2}t_{2}40 × 25 = 50 × t_{2} 4
t_{2} = 5 hrs.
 A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot at the rate 4 kmph and partly on bicycle at the rate 9 kmph. The distance travelled on foot is

 16 km
 14 km
 17 km
 15 km

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Distance travelled by farmer on foot = x km (let)
∴ Distance covered by cycling = (61–x ) km.Time = Distance Speed
According to the question,x + 61 − x = 9 4 9 ⇒ 9x + 61 × 4 − 4x = 9 9 × 4
⇒ 5x + 244 = 9 × 9 × 4 = 324
⇒ 5x = 324 – 244 = 80⇒ x = 80 = 16 km. 5
Second Method :
Here, t = 9, x= 61
u = 4, v = 9Time taken = vt − x v − u = 9 × 9 − 61 9 − 4 = 20 = 4 hrs. 5
Distance travelled
= 4 × 4 = 16 kmCorrect Option: A
Distance travelled by farmer on foot = x km (let)
∴ Distance covered by cycling = (61–x ) km.Time = Distance Speed
According to the question,x + 61 − x = 9 4 9 ⇒ 9x + 61 × 4 − 4x = 9 9 × 4
⇒ 5x + 244 = 9 × 9 × 4 = 324
⇒ 5x = 324 – 244 = 80⇒ x = 80 = 16 km. 5
Second Method :
Here, t = 9, x= 61
u = 4, v = 9Time taken = vt − x v − u = 9 × 9 − 61 9 − 4 = 20 = 4 hrs. 5
Distance travelled
= 4 × 4 = 16 km
 The distance between 2 places R and S is 42 km. Anita starts from R with a uniform speed of 4 km/h towards S and at the same time Romita starts from S towards R also with some uniform speed. They meet each other after 6 hours. The speed of Romita is

 18 km/hour
 6 km/hour
 20 km/hour
 8 km/hour
 None of these

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Speed of Romita = x kmph
(let)
Distance = Speed × Time
According to the question,
4 × 6 + x × 6 = 42
⇒ 6x = 42 – 24 = 18
⇒ x = 18 ÷ 6 = 3 kmph
Second Method :
Distance from R to S = S_{1}t_{1}+S_{2}t_{2}
42 = 4 × 6 + x × 6
6x = 18 x = 3 km/hr.Correct Option: E
Speed of Romita = x kmph
(let)
Distance = Speed × Time
According to the question,
4 × 6 + x × 6 = 42
⇒ 6x = 42 – 24 = 18
⇒ x = 18 ÷ 6 = 3 kmph
Second Method :
Distance from R to S = S_{1}t_{1}+S_{2}t_{2}
42 = 4 × 6 + x × 6
6x = 18 x = 3 km/hr.
 A journey takes 4 hours 30 minutes at a speed of 60 km/hr. If the speed is 15 m/s, then the
journey will take

 5 hours
 5 hours 30 minutes
 6 hours
 6 hours 15 minutes

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60 kmph = 60 × 5 m/sec 18 = 50 m/sec. 3 ∴ Speed ∝ 1 Time
⇒ S_{1} × T_{1} = S_{2} × T_{2}⇒ 50 × 9 = 15 × T_{2} 3 2 ⇒ T_{2} = 75 = 5 hours 15
Second Method :Here, S_{1} = 60, t_{1} = 4 1 = 9 2 2 S_{2} = 15 × 18 = 54 5
S_{1}t_{1} = S_{2}t_{2}60 × 9 = 54 × t_{2} 2 t_{2} = 270 = 5 hours 54 Correct Option: A
60 kmph = 60 × 5 m/sec 18 = 50 m/sec. 3 ∴ Speed ∝ 1 Time
⇒ S_{1} × T_{1} = S_{2} × T_{2}⇒ 50 × 9 = 15 × T_{2} 3 2 ⇒ T_{2} = 75 = 5 hours 15
Second Method :Here, S_{1} = 60, t_{1} = 4 1 = 9 2 2 S_{2} = 15 × 18 = 54 5
S_{1}t_{1} = S_{2}t_{2}60 × 9 = 54 × t_{2} 2 t_{2} = 270 = 5 hours 54
 Sriya with her family travelled from Bolpur to Suri by car at a speed of 40 km/hr and returned to Bolpur at a speed of 50 km/hr. The average speed for the whole journey is


44 4 km/hr 9  45 km/hr

45 1 km/hr 2  44.78 km/hr


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Average speed of journey = 2xy kmph x + y ⇒ 2 × 40 × 50 = 2 × 40 × 50 40 + 50 90 ⇒ 400 = 44 4 kmph 9 9 Correct Option: A
Average speed of journey = 2xy kmph x + y ⇒ 2 × 40 × 50 = 2 × 40 × 50 40 + 50 90 ⇒ 400 = 44 4 kmph 9 9