Ex. 1. How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr? Sol. Aditya's speed = 20 km/hr = {20 * 5/18} m/sec = 50/9 m/sec

∴Time taken to cover 400 m= { 400 * 9/50 } sec =72 sec = 1 12/60 min = 1 1/5 min.

Ex. 2. A cyclist covers a distnce of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist? Sol. Speed = { 750/150 } m/sec =5 m/sec = { 5 * 18/5 } km/hr =18km/hr

Ex. 3. A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds. Sol. Let the distance covered in 1 leap of the dog be x and that covered in 1 leap of the hare by y. Then , 3x = 4y ⇒ x = 4/3 y ⇒ 4x = 16/3 y. ∴ Ratio of speeds of dog and hare = Ratio of distances covered by them in the same time = 4x : 5y = 16/3 y : 5y =16/3 : 5 = 16:15

Ex. 4.While covering a distance of 24 km, a man noticed that after walking for 1 hour and 40 minutes, the distance covered by him was 5/7 of the remaining distance. What was his speed in metres per second? Sol. Let the speed be x km/hr. Then, distance covered in 1 hr. 40 min. i.e., 1 2/3 hrs = 5x/3 km Remaining distance = { 24 - 5x/3 } km. ∴ 5x/3 = 5/7 { 24 - 5x/3 } ⇔ 5x/3 = 5/7 { (72-5x)/3 } ⇔ 7x =72-5x ⇔ 12x = 72 ⇔ x=6 Hence speed = 6 km/hr ={ 6 * 5/18 } m/sec = 5/3 m/sec = 1 2/3

Ex. 5.An aeroplane files along the four sides of a square at the speeds of 200,400,600 and 800km/hr.Find the average speed of the plane around the field. Sol. : Let each side of the square be x km and let the average speed of the plane around the field by y km per hour then , x/200+x/400+x/600+x/800=4x/y ⇔25x/2500 ⇔4x/y ⇔y=(2400*4/25)=384 hence average speed =384 km/hr

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Ex. 1. How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr?

Sol. Aditya's speed = 20 km/hr = {20 * 5/18} m/sec = 50/9 m/sec∴Time taken to cover 400 m= { 400 * 9/50 } sec =72 sec = 1 12/60 min = 1 1/5 min.

Ex. 2. A cyclist covers a distnce of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?

Sol. Speed = { 750/150 } m/sec =5 m/sec = { 5 * 18/5 } km/hr =18km/hrEx. 3. A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds.

Sol. Let the distance covered in 1 leap of the dog be x and that covered in 1 leap of the hare by y.Then , 3x = 4y ⇒ x = 4/3 y ⇒ 4x = 16/3 y.

∴ Ratio of speeds of dog and hare = Ratio of distances covered by them in the same time

= 4x : 5y = 16/3 y : 5y =16/3 : 5 = 16:15

Ex. 4.While covering a distance of 24 km, a man noticed that after walking for 1 hour and 40 minutes, the distance covered by him was 5/7 of the remaining distance. What was his speed in metres per second?

Sol. Let the speed be x km/hr.Then, distance covered in 1 hr. 40 min. i.e., 1 2/3 hrs = 5x/3 km

Remaining distance = { 24 - 5x/3 } km.

∴ 5x/3 = 5/7 { 24 - 5x/3 } ⇔ 5x/3 = 5/7 { (72-5x)/3 } ⇔ 7x =72-5x

⇔ 12x = 72 ⇔ x=6

Hence speed = 6 km/hr ={ 6 * 5/18 } m/sec = 5/3 m/sec = 1 2/3

Ex. 5.An aeroplane files along the four sides of a square at the speeds of 200,400,600 and 800km/hr.Find the average speed of the plane around the field.

Sol. :Let each side of the square be x km and let the average speed of the plane around the field by y km per hour then ,

x/200+x/400+x/600+x/800=4x/y ⇔25x/2500 ⇔4x/y ⇔y=(2400*4/25)=384

hence average speed =384 km/hr