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.
Answers
Answered by
86
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
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
santy2:
Ajeet's speed cannot be (x+2) km/hr
Answered by
256
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.
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.
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