Question

plz tell me the answer of this question ☝️☝️ ..fast..​

Answer 1

Both answers are same

Let the actual speed of the man be x km/hr and y be the actual time taken by him in hours.

So, we know that

Distance covered = speed x distance

⇒ Distance = x × y = xy …………(i)

First condition from the question says that,

If the speed of the man increase by 1/2 km/hr, the journey time will reduce by 1 hour.

Showing this using variables, we have

⇒ When speed is (x + 1/2) km/hr, time of journey = y – 1 hours

Now,

Distance covered = (x + 1/2) x (y – 1) km

Since the distance is the same i.e xy we can equate it, [from (i)] xy = (x + 1/2) x (y – 1)

And we finally get,

-2x + y – 1 = 0 ………………(ii)

From the second condition of the question, we have

If the speed reduces by 1 km/hr then the time of journey increases by 3 hours.

⇒ When speed is (x-1) km/hr, time of journey is (y+3) hours

Since, the distance covered = xy [from (i)]

xy = (x-1)(y+3)

⇒ xy = xy – 1y + 3x – 3

⇒ xy = xy + 3x – 1y – 3

⇒ 3x – y – 3 = 0 ……………… (iii)

From (ii) and (iii), the value of x can be calculated by

(ii) + (iii)

⇒ x – 4 = 0

x = 4

Now, y can be obtained by using x = 4 in (ii) -2(4) + y – 1 = 0

⇒ y = 1 + 8 = 9

Hence, putting the value of x and y in equation (i), we find the distance

Distance covered = xy

= 4 × 9

= 36 km

Thus, the distance is 36 km and the speed of walking is 4 km/hr.