A boy travels from his home to his school at a speed 10 km/h. He returns back from his school to his home at a speed x km/h such that average speed during entire journey is 12 km/h. Value of x is
Answers
Given info : A boy travels from his home to his school at a speed 10 km/h. He returns back from his school to his home at a speed x km/h such that average speed during entire journey is 12 km/h.
To find : the value of x is...
solution : let the distance between home and school of the boy is d km.
case 1 : the boy travels from his home to his school at a speed 10 km/h.
so time taken to travel his home to school, t₁ = distance/speed = d/10 hrs
case 2 : he returns from his school to his home at a speed of x km/h.
time taken to travel from his school to home, t₂ = distance/speed = d/x hrs
here average speed of the boy is 12 km/h.
we know, average speed = total distance/total time taken.
⇒ 12 = (d km + d km)/(t₁ + t₂)
= 2d/(d/10 + d/x) = 20x/(x + 10)
⇒ 12 = 20x/(x + 10)
⇒ 12x + 120 = 20x
⇒ 120 = 8x
⇒ x = 15
therefore the value of x is 15 km/h.