Question

Aryan covers a distance of 1 km from A to B. While returning, his speed is 3 km/hr more than first half of the journey. The total time taken for the journey is 0.5hr. Find the speed for the first half and second half of the journey.​

Answer 1

The correct answer is  the speed of first half is 3 km/hr and speed of second half is 6 km/hr.

Given: Total distance = 1 km.

Total time to cover the journey = 0.5 hr.

To Find: Speed of first and second half of journey.

Solution:

Let the speed of first half = v

Speed of second half = v+3

$Speed=\frac{Distance}{Time}$

$Time=\frac{Distance}{Speed}$

Equation for first half journey.

Let the time taken to cover first half = $T_{1}$

$T_{1}=\frac{1}{v}$

Equation for second half journey.

Let the time taken to cover second half = $T_{2}$

$T_{2}=\frac{1}{v+3}$

Total time = $T_{1} +T_{2}$

$\frac{1}{2}$ = $\frac{1}{v} +\frac{1}{v+3}$

$\frac{1}{2} =\frac{v+3+v}{v(v+3)}$

v(v+3) = 2(2v + 3)

$v^{2} +3v=4v+6$

$v^{2} -v-6=0$

$v^{2} +2v-3v-6=0\\ v(v+2)-3(v+2)$

(v-3)(v+2)

v = 3, -2

As speed cannot be negative so speed is 3 km/hr.

Speed of second half = v+3 = 3+3 = 6

Hence, the speed of first half is 3 km/hr and speed of second half is 6 km/hr.

#SPJ1

Answer 2

Step-by-step explanation:

LET SPEED OF FIRST HALF IS X

SPEED OF SECOND HALF IS X+3

TIME DISTANCE/SPEED

TIME 1+ TIME 2

1/X+ 1/X+3 = 1/2

2x+3/ x^2+3x = 1/2

4x+6= x^2+3x

x=3 or x=-2

speed of first half is 3

speed of second half is 3+3=6