a motorboat whose speed is 24 km per hour and is still in water 1 hour more to go 32 km upstream than to returns trains to the same spot find the speed of the spot
Answers
Answer:
The answer is 8 km/hr i.e. the speed of the stream.
Step-by-step explanation:
Let speed of the stream be x km/hr
Speed of the motorboat = 24 km/hr
Total distance = 32 km
then, speed of boat moving upstream = 24 - x
speed of the boat moving downstream = 24 + x
[as we know that distance/speed = time.]
∴ time taken by motorboat to go downstream = 32/24 + x
time taken by motorboat to go upstream = 32/24 - x
According to given question ,
32/24 + x + 1 = 32/24 - x
=32 + 24 + x/24 + x = 32/24 - x
=56 +x/24 + x = 32/24 - x
=56 + x ( 24 - x) = 32(24 + x)
=1344 - 56x + 24x - x² = 768 + 32x
=1344 - 768 - 32x - 32x - x² = 0
= 576 - 64x - x² = 0
∴ x² + 64x - 576 = 0
[Solve the given equation by splitting the middle term method, using 8 & 72 as factors]
x² + 64x - 576 = 0
= x² + 72x - 8x - 576 = 0
= x ( x + 72) - 8 (x + 72) = 0
= ( x - 8) ( x + 72)
∴ x - 8 = 0 ⇒ x = 8 km/hr
x + 72 = 0 ⇒ x = - 72km/ hr [ Speed cannot be negative]
∴ Speed of the stream = 8 km/hr.