Question

while covering a distance of 30km, Ajeet takes 2 hrs more than Amit. If Amit doubles his speed, he would take 1 hr less than Amit. Find the speed of their walking.

Answer 1

The formula for calculating speed is: 

Speed = total distance traveled/time taken.

Let the speed of Amit be x km/hr
And that of Ajeet be (x+2) km/hr

If the speed of Amit doubles it will be : 

x × 2 = 2x km/hr

Time taken =  distance traveled / speed

The distance traveled by both is 30 km,

Amit's speed  = 2xkm/hr

Ajeet's speed  = x+2 km/hr

Since time = distance / speed , we can use the distance covered and the speed equations to write an expression for Amit taking 1 hour less than Ajeet and then solve for x.

The expression, using time = distance/speed, is:

30km/2x = 30km/(x+2)km/hr + 1hr

Multiply all through by 2x(x+2) to eliminate the denominators

⇒⇒   30x + 60 = 60x + 2x² + 4x

⇒⇒  -2x² + 30x - 60x + 60 - 4x = 0

⇒⇒  2x² - 30x + 60x - 60 + 4x= 0

⇒⇒ 2x² + 34 x - 60 = 0

x = √409/2 - 17/2

= 10.1 - 8.5
 
x = 1.6 km/hr

That means,  Amit's speed = x = 1.6 km/hr
             and, Ajeet's speed = x+2 = 1.6+2 = 3.6km/r    
 

Answer 2

Solution :-

Let time taken by Amit to cover the distance of 30 km be x hour

Then, time taken by Ajeet to cover the distance of 30 km will be (x + 2) hour

Speed of Amit = 30/x km/hr

Speed of Ajeet = 30/(x + 2) km/hr

Now, according to the question.

If Ajeet doubles his speed, time taken by Ajeet to cover a distance of 30 km

= 30/[2*30/(x + 2)]

= (x + 2)/2hr

Now, (x + 2)/2 = x - 1

⇒ (x + 2) = 2x - 2

⇒ x - 2x = - 2 - 2

⇒ - x = - 4

⇒ x = 4

So, Amit takes 4 hours to cover 30 km.

Time taken by Ajeet to cover 30 km = 4 + 2 = 6 hr

Now, speed of Amit = Distance/Time

= 30/4 

= 7.5 km/hr

Speed of Ajeet = 30/6 

= 5 km/hr

So, speed of Amit is 7.5 km/hr and speed of Ajeet is 5 km/hr

Answer.