Chapter - 16
TIME AND DISTANCE
Distance travelled = speed x time
Speed = distance / time
Time = distance / speed
If the time taken, to travel two distances with different speeds, is equal then
Average speed = (speed1 + speed 2) / 2
average speed = total distance travelled / total time taken
if two distances travelled are equal and two speeds are x km /hr and y km / hr
then average speed =
if 3 equal distances are travelled at speeds x km /hr, ykm/ hr and z km/hr respectively then average speed =
FORMULAE FOR QUESTIONS ON TRAINS
So the time taken to pass a pole
So time taken by the train (length T) to pass a platform (length A) = T+A / Speed
The relative speed if the direction of the trains is the same = (x – y) km/ hr
The relative speed if the direction of trains is opposite to each other
= (x+y) km /hr
Example 1: A bike crosses a bridge at a speed of 180 km/hr. what will be length of the bridge if the bike takes 3 minutes to cross the bridge.
Speed = 180 km/hr = (180 x 5) / 18 = 50 meters / sec.
Time = 3 x 60 = 180 seconds.
So length of the bridge
50 X 180 meters
= (50 x 180) / 1000 km
= 9 km
Ex. 2: A person covers km in 6 hours. What distance will he cover in 5 hours.
= 102/30 km/hr
Distance covered in 5 hours = (102/30) x 5 = 17 km
Ex. 3: Two persons are moving in the direction opposite to each other. The speeds of the two persons are 8 km/hr and 5 km per hour. Find their relative speed wrt each other
So required relative speed = 8 + 5 = 13 km/hr
Ex. 4: A bus covers a distance of 600 km with a speed of 30 km/hr. How much time will it take to cover the distance.
= 600 / 30 = 20 hours
Ex. 5: Two trains A and B are moving at the speeds in the ratio of 2 : 5. Find the ratio of the time taken to travel the same distance.
i.e. since speeds are 2 : 5
so time must be 5 : 2
Ex. 6: Prem can cover a certain distance in 42 minutes by covering 2/3 of the distance at 4 km/hr and the rest at 5 km/hr. find the total distance.
So as per the given condition.
Distance / speed + distance / speed = total time
Or (2x/3) x ¼ + (x/3) x (1/5) = 42/60
Or x/2 + x/5 = 42/20
7x/10 x= 42/20
X = 3 km
Example 7: A man completes 60 km of a journey at 12 km / hr and the remaining 80 km of the journey in 5 hours. Find the average speed for the whole journey.
Total time taken = 5 hours + 5 hours = 10 hours
So average speed for the whole journey = 140/10
= 14 km/hr
Time taken during the first part to cover 60 km = 60 / 12= 5 hours
Time taken to cover the second part = 5 hrs
And the speed during 2nd part = 80/5 = 16 km/hr
So the time taken during the two journeys is equal
So average speed = (12 km/hr + 16 km/hr) / 2 = 28/2
= 14 km/hr
Ex 8: A certain distance is covered at a certain speed. If half the distance is covered in double the time, the ratio of two speeds is
S = X / T
Now in the 2nd case distance is x/2
And time is = 2 T
The speed is
The ratio in the speed is X/T = X / 4T
Or 1 : ¼ or 4 : 1
Ex. 9: A bullock cart has to cover a distance of 40 km in 5 hours. If it covers half of the journey in 3/5 th of the time, what should be its speed to cover the remaining distance in the left over time.
20/2 = 10 km/hr
Ex. 10: A car travels from A to B at a speed of 58 km/hr and travels back from B to A at the speed of 42 km/hr. what is average speed of the car in covering the distance both ways.
Average speed =
Ex. 11: The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than the time taken by B to reach a destination. In what time doesA reach the destination
Then time taken by B = (x – 20/60) hours
Or (x – 1/3) hours
Ratio of speeds = inverse ratio of time
or x = 4/3 hours
Example 12: A train 100 meter long is running at a speed of 30 km/hr. Find the time taken by the train to pass a man standing near the railway line.
Distance to be travelled to pass the man = 100 meter
So time to pass the man = distance / speed =
Ex. 13: A train is moving at a speed of 66 km/hr. if the length of the train is 55 metre, how long will it take to cross a plat form 165 meter long.
meter / sec
Distance to be covered in crossing the palt form
= 55 + 165 = 220 meter.
Time required = (220) / (55 /3)
Ex. 14: A train crosses a platform in 20 seconds but a man standing on the platform in 8 seconds. Length of the platform is 180 meters. Find the length of the train and its speed
Time taken to cross the man = 8 sec.
20 – 8 = 12 sec is the time taken by the train to travel the distance equal to platform.
The train travels 180 meter in 12 seconds
So its speed is 180/12 = 15 m/sec.
And the length of the train = distance travelled in
8 sec. = 15 x 8 = 120 meter
Example 15: A train 200 m long is running at a speed of 68 km/hr. in what time will it pass a man who is running at 8 km/hr in the same direction in which train is going
To cross the man the train has to travel a distance equal to its length
60 km/hr = (60 x 5)/18 m/ sec. = 300/ 18 meter/ sec.
So = 12 minutes
Ex. 16: A train 165 meter in length is running with a speed of 59 km/hr. in what time will it pass a man who is running at a speed of 7 km/hr in the direction opposite to that in which the train is going?
Or (66 x 5)/18 meter / sec.
The time taken by the train to cross the man
Ex. 17: Two trains are running towards each other at the rate of 42 km/hr and 30 km/hr. The length of the trains is 120 meter and 80 meters respectively. In what time will they cross each other from the moment they meet.
= 72 km/hr
= 72 x 5/18 = 20 m / sec
Time taken by the trains to pass each other = sum of their lengths divided by the relative speed
Ex. 18: Two trains 100 meters and 80 meters long are running in the same direction with speeds 90 km/hr and 54 km/hr respectively. In how much time will the first train cross the second train.
= 36 km/h = 36 x 5/18 = 10 meter / second
Time taken by the trains to cross each other
=sum of their lengths / relative speed
= (100+80) / 10 = 180/10 = 18 sec
Ex. 19: A train 100 meters long takes 6 seconds to cross a man walking at 10 km/hr in a direction opposite to that of the train. Find the speed of the train.
= (x + 10) x (5/18) meter / second
Now 6 seconds
Or 100 = 6 x (x + 10) x 5/18 = 5/3 (x + 10)
Or x + 10 = (100 x 3) / 5 = 60 or x = 50 km/hr
Ex. 20: A train running at 54 km/hr. takes 25 seconds to pass a platform and 15 seconds to pass a man walking at 6 km/h in the same direction in which train is going. Find the length of the train and the length of the platform.
Speed of the train w.r.t the man = 54 – 6 = 48 km/ph
= 48 x 5/18 = 40/3 meter / seconds
In passing the man the train covers its own length with the relative speed.
So the length of the train = Relative speed x time
= (40/3 x 15) m = 200 m.
Speed of the train = 54 x 5/18 = 15 m/second.
Distance travelled to pass the platform = x + y
So x + y = 200 + y
So (200 + y) / 15 = 25
Or y + 200 = 375
Or y = 175 meters.