The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km/hr
Answers
Distance = same 150 miles 1
original time – time with increased speed = 2.5 hour
t=d/t
150 / x - 150 / ( x + 10 ) = 2.50
LCD= x ( x + 10 )
multiply by LCD
150 ( x + 10 ) - 150 x = 2.5 x ( x + 10 )
150 x + 1500 - 150 x = 2.5 X^2 + 25 x
1500 = 2.5 X^2 + 25 x
2.5 X^2 + 25 x - -1500 = 0
Find roots of the quadratic equation
a= 2.5 b= 25 c= -1500
x1= ( -25 + sqrt( 625 + 15000 )) / 5
x1=( -25 + 125 )/ 5
x1= 20
x2= ( -7 - sqrt( 49 - 20 ) / 2
x2=( -25 - 125 )/ 5
x2= -30
Ignore negative
forward speed = 20 kmph
return speed = 30 kmph
Step-by-step explanation:
⇒ Distance given =150km
⇒ Let the forward speed be x and the return speed will be x+10
We know that, Time=
speed
Distance
∴
x
150
=
x+10
150
+2.5
⇒ 150(x+10)−150x=2.5×x(x+10)
⇒ 150x+1500−150x=2.5x
2
+25x
⇒ 2.5x
2
+25x−1500=0
⇒ 25x
2
+250x−15000=0
⇒ x
2
+10x−600=0
⇒ x
2
+30x−20x−600=0
⇒ x(x+30)−20(x+30)=0
⇒ (x+30)(x−20)=0
The value of cannot be negative.
∴ Forward speed will be 20km/hr
⇒ Return speed =20+10=30km/hr
⇒ The required product =20×30=600km/hr
hope it helps you brother