Question

p and q each walks 48 km . the sum of their speed is 8 kmph and the sum of the time taken by them is 24 hours. the ratio of the speed of p to that of q is equal to

Answer 1

Let the speed of P be x km/hr.

Given that the sum of their speed is 8 km/hr = > Speed of Q = (8 - x) km/hr.

Given that P and Q each walks 48 km.

= > (48/x) + (48/8 - x).

Given that Sum of the time taken by them is 24 hours.

$= > \frac{48}{x} + \frac{48}{8 - x} = 24$

= > 48(8 - x) + 48x = 24x(8 - x)

= > 384 - 48x + 48x = 192x - 24x^2

= > 384 = 192x - 24x^2

= > -24x^2 + 192x - 384 = 0

= > -24(x^2 - 8x + 16) = 0

= > x^2 - 4x - 4x + 16 = 0

= > x(x - 4) - 4(x - 4) = 0

= > (x - 4)(x - 4) = 0

= > (x - 4)^2 = 0

= > x = 4.

The speed of P = 4 km/hr.

Speed of Q = (8 - x)

= (8 - 4)

= 4.

Therefore, the ratio of speed of p to that of q = 4 : 4.

Hope it helps!

Answer 2

Let the speed of the P and Q be x and y km/hr.

∴ x + y = 8

∴ x = 8 - y

Distance covered by P and Q = 48 km

Time taken by P + Time taken by Q = 24 hrs.

∴ t₁ + t₂ = 24 hrs.

Now,

Speed of the P = x = 8 - y

∴ Time taken by P = 48/8 - y

Speed of the Q = y

∴ Time taken by Q = 48/y

∴ 48/8 - y + 48/y = 24

48y + 48(8 - y) = 24(8 - y)(y)

48y + 384 - 48y = 192y - 24y²

24y² - 192y + 384 = 0

6y² - 48y + 96 = 0

2y² - 16y + 32 = 0

y² - 8y + 16 = 0

y² - 4y - 4y + 16 = 0 [Splitting the middle term]

y(y - 4) - 4(y - 4) = 0 [Zero Product Rule]

(y - 4)(y - 4) = 0

y = 4

∴ Speed of the Q = 4 km/hr.

∴ Speed of the P = 8 - 4 = 4 km/hr.

∴ Ratio of the speed = 1 : 1

Hope it helps