Question

The time taken by a person to cover 150 km was 2whole 1 / 2 hrs more than the time taken in the return journey. If he returned at speed of 10 km / hr more than the speed while going. Find the speed per hr in each direction.

Answer 1

Hey there !!


➡ Given:-

→ distance  = 150km.

→ Time = $2 \frac{1}{2} = 2.5 hrs .$


➡ To find :-

→ The speed per hour in each direction.


➡ Solution :-

→ Let the forward speed be x,

And, the return speed will be x + 10.

▶ We know that,

→ Time = distance/speed

=> $\frac{150}{x} = \frac{150}{x+10} + 2.5$

=> $\frac{150}{x} = \frac{150 + 2.5 ( x + 10 ) }{x+10}$

=> 150( x + 10 ) = x( 150 + 2.5( x + 10 ).

=> 150( x + 10 ) = 150x + 2.5x( x + 10 ) .

=> 150 (x + 10) - 150x = 2.5 x ( x + 10 )

=> 150x + 1500 - 150x = 2.5x² + 25x .

=> 1500 = 5( x²/2 + 5x ).

=> 1500/5 = ( x² + 10x )/2 .

=> 300 × 2 = x² + 10x.

=> x² + 10x - 600 = 0

=> x² + 30x - 20x - 600 = 0.

=> x( x + 30 ) - 20( x + 30 ) = 0.

=> (x+30) (x-20) = 0

=> x + 30 = 0 | x - 20 = 0.

=>  x = -30 and x = 20.

The value of x cannot be negative.

Forward speed will be 20km/hr.

Return speed will be ( x + 10 = 20 + 10 ) 30 km/hr.

✔✔ Hence, it is solved ✅✅.

____________________________________



THANKS


#BeBrainly.

Answer 2

Going Journey Distance = 150 km

Returning Journey Distance = 150 km

Let the Time take by the person in the Return Journey be : J Hours

Given : The Time taken by the Person to Cover 150 km was 2.5 hrs more than the Time taken in the Return Journey.

⇒ Time taken by the Person while Going is : (J + 2.5) hrs

We know that : $Speed = \frac{Distance-Traveled }{Time-Taken}$

⇒ Speed of the person while Going = $\frac{150}{J + 2.5}$

⇒ Speed of the person while returning = $\frac{150}{J}$

Given : His Returning Speed is 10km/hr more than while Going.

⇒ $\frac{150}{J + 2.5} + 10 = \frac{150}{J}$

⇒ $\frac{175 + 10J}{J + 2.5} = \frac{150}{J}$

⇒ 10J² + 175J = 150J + 375

⇒ 10J² + 25J - 375 = 0

⇒ 2J² + 5J - 75 = 0

⇒ 2J² + 15J - 10J - 75 = 0

⇒ 2J(J - 5) + 15(J - 5) = 0

⇒ (J - 5)(2J + 15) = 0

⇒ J = 5 or J = -15/2

As Time Cannot be Negative

⇒ J = 5 hrs is True

⇒ Speed of the Person while Going = 150/7.5 = 20km/hr

⇒ Speed of the Person while Returning = 150/5 = 30km/hr