Speed, Time and Distance
- 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
-
View Hint View Answer Discuss in Forum
60 kmph = 
60 × 5 
m/sec 18 = 50 m/sec. 3 ∴ Speed ∝ 1 Time
⇒ S1 × T1 = S2 × T2⇒ 50 × 9 = 15 × T2 3 2 ⇒ T2 = 75 = 5 hours 15
Second Method :Here, S1 = 60, t1 = 4 1 = 9 2 2 S2 = 15 × 18 = 54 5
S1t1 = S2t260 × 9 = 54 × t2 2 t2 = 270 = 5 hours 54 Correct Option: A
60 kmph = 60 × 5 m/sec 18 = 50 m/sec. 3 ∴ Speed ∝ 1 Time
⇒ S1 × T1 = S2 × T2⇒ 50 × 9 = 15 × T2 3 2 ⇒ T2 = 75 = 5 hours 15
Second Method :Here, S1 = 60, t1 = 4 1 = 9 2 2 S2 = 15 × 18 = 54 5
S1t1 = S2t260 × 9 = 54 × t2 2 t2 = 270 = 5 hours 54
- 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
-
View Hint View Answer Discuss in Forum
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 = S1t1+S2t2
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 = S1t1+S2t2
42 = 4 × 6 + x × 6
6x = 18 x = 3 km/hr.
- 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
-
View Hint View Answer Discuss in Forum
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
- 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 ?
-
View Hint View Answer Discuss in Forum
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, S1 = 40, t1 = 6 15 = 25 60 4
S2 = 50, t2 = ?
S1t1 = S2t240 × 25 = 50 × t2 4
t2 = 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, S1 = 40, t1 = 6 15 = 25 60 4
S2 = 50, t2 = ?
S1t1 = S2t240 × 25 = 50 × t2 4
t2 = 5 hrs.
- A student starting from his house walks at a
school 6 minutes late. Next day starting atspeed of 2 1 km/hour and reaches his 2
the same time he increases his speed by 1 km/hour and reaches 6 minutes early. The distance between the school and his house is
-
View Hint View Answer Discuss in Forum
Distance between school and house = x km (let)
Time = Distance Speed
According to the question,x − x = 6 + 6 = 1 5/2 7/2 60 5
(Difference of time = 6 + 6 =12 minutes)⇒ 2x − 2x = 1 5 7 5 ⇒ 14x − 10x = 1 ⇒ 4x = 1 35 5 35 5 ⇒ 4x = 35 = 7 5 ⇒ x = 7 = 1 3 km. 4 4
Second Method :Here, S1 = 2 1 , t1 = 6 2 S2 = 3 1 , t2 = 6 2 Distance = (S1 × S2)(t1 + t2) S2 − S1 = 
5 × 7 (6 + 6) 2 2 7 - 5 2 2 = 35 × 12 4 60 = 7 = 1 3 km 4 4 Correct Option: C
Distance between school and house = x km (let)
Time = Distance Speed
According to the question,x − x = 6 + 6 = 1 5/2 7/2 60 5
(Difference of time = 6 + 6 =12 minutes)⇒ 2x − 2x = 1 5 7 5 ⇒ 14x − 10x = 1 ⇒ 4x = 1 35 5 35 5 ⇒ 4x = 35 = 7 5 ⇒ x = 7 = 1 3 km. 4 4
Second Method :Here, S1 = 2 1 , t1 = 6 2 S2 = 3 1 , t2 = 6 2 Distance = (S1 × S2)(t1 + t2) S2 − S1 = 5 × 7 (6 + 6) 2 2 7 - 5 2 2 = 35 × 12 4 60 = 7 = 1 3 km 4 4
