Speed, Time and Distance
- A man travelled a distance of 80 km in 7 hrs partly on foot at the rate of 8 km per hour and partly on bicycle at 16km per hour. The distance travelled on the foot is
-
View Hint View Answer Discuss in Forum
Journey on foot = x km
Journey on cycle = (80 – x) km∴ x = 80 − x = 7 8 16 ⇒ 2x + 80 − x = 7 16
⇒ x + 80 = 16 × 7 = 112
⇒ x = 112 - 80 = 32 km.
Second Method :
Here, x = 80, t = 7
u = 8, v = 16Time = 
vt − x 
v − u = 16 × 7 − 80 16 − 8 = 112 − 80 8 = 32 = 4 hrs 8
Distance travelled
= 4 × 8 = 32 kmsCorrect Option: A
Journey on foot = x km
Journey on cycle = (80 – x) km∴ x = 80 − x = 7 8 16 ⇒ 2x + 80 − x = 7 16
⇒ x + 80 = 16 × 7 = 112
⇒ x = 112 - 80 = 32 km.
Second Method :
Here, x = 80, t = 7
u = 8, v = 16Time = vt − x v − u = 16 × 7 − 80 16 − 8 = 112 − 80 8 = 32 = 4 hrs 8
Distance travelled
= 4 × 8 = 32 kms
- A car driver leaves Bangalore at 8.30 A.M. and expects to reach a place 300 km from Bangalore at 12.30 P.M. At 10.30 he finds that he has covered only 40% of the distance. By how much he has to increase the speed of the car in order to keep up his schedule?
-
View Hint View Answer Discuss in Forum
Distance covered by car in 2 hours
= 300 × 40 = 120 km 100
Remaining distance = 300 – 120 = 180 km
Remaining time = 4 – 2 = 2 hours∴ Required speed = 180 = 90 kmph 2 Original speed of car = 120 = 60 kmph 2
∴ Required increase in speed
= 90 – 60 = 30 kmphCorrect Option: D
Distance covered by car in 2 hours
= 300 × 40 = 120 km 100
Remaining distance = 300 – 120 = 180 km
Remaining time = 4 – 2 = 2 hours∴ Required speed = 180 = 90 kmph 2 Original speed of car = 120 = 60 kmph 2
∴ Required increase in speed
= 90 – 60 = 30 kmph
- A man is walking at a speed of 10 kmph. After every km, he takes a rest for 5 minutes. How much time will he take to cover a distance of 5 km?
-
View Hint View Answer Discuss in Forum
Time taken in covering 5 Km = 5 = 1 hour 10 2
= 30 minutes
That person will take rest for four times.
∴ Required time
= (30 + 4 × 5) minutes
= 50 minutesCorrect Option: B
Time taken in covering 5 Km = 5 = 1 hour 10 2
= 30 minutes
That person will take rest for four times.
∴ Required time
= (30 + 4 × 5) minutes
= 50 minutes
- 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
-
View Hint View Answer Discuss in Forum
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, S1 = 10 km/min 12 = 10 × 60km/hr 12 = 50 km/hr, t1 = 12 = 1 hr 60 5
S2 = 45 km/hr, t2 = ?
S1t1 = S2t250 × 1 = 45 × t2 5 t2 = 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, S1 = 10 km/min 12 = 10 × 60km/hr 12 = 50 km/hr, t1 = 12 = 1 hr 60 5
S2 = 45 km/hr, t2 = ?
S1t1 = S2t250 × 1 = 45 × t2 5 t2 = 10 × 60 min 45 = 40 min 3
- Motor-cyclist P started his journey at a speed of 30 km/hr. After 30 minutes, motor-cyclist 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 ?
-
View Hint View Answer Discuss in Forum
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
