A motor boat whose speed is 18 km/hr in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot.find the speed of the steam
Answers
Answer:
Complete step-by-step Solution:
Let the speed of the stream be x km/hr.
Let the time taken to travel 24 km downstream by motor boat be t hours.
⇒⇒The time taken to travel 24 km upstream by motor boat = (t + 1) hours.
The given speed of the motor boat in the still water is equal to 18 km/hr.
The given distance travelled by motor boat is equal to 24 km.
We know that the formulae
The upstream speed of the motor boat = Speed of the motor boat in still water – Speed of the stream
= 18 - x
The downstream speed of the motor boat = Speed of the motor boat in the still water + Speed of the stream
= 18 + x
We know that the formula for the distance travelled by a boat = Net speed of the boat ××time taken to travel
By substituting given values in the above formula for the boat travelled 25 km upstream in (t + 1) hours, we get
24=(18−x)(t+1)24=(18−x)(t+1)
24=18t+18−xt−x24=18t+18−xt−x
xt+x=18t−6xt+x=18t−6
x=18t−6t+1x=18t−6t+1 …….(1)
By substituting given values in the above formula for the boat travelled 25 km downstream in t hours, we get
24=(18+x)t24=(18+x)t
By substituting the equation (1) in the above equation we get
24t+24=36t2+12t24t+24=36t2+12t
36t2−12t−24=036t2−12t−24=0
3t2−t−2=03t2−t−2=0
3t2−3t+2t−2=03t2−3t+2t−2=0
(3t+2)(t−1)=0
The time taken to travel 24 km downstream by motor boat = 1 hour.
By substituting the t value in equation (1) we get
x=18(1)−61+1x=18(1)−61+1
x=122=6x=122=6km/hr.
∴∴ The speed of the stream = 6 km/hr.
Let the speed of the stream be x km\hr.
The speed of the boat upstream = (18 - x) km/hr
The speed of the boat downstream = (18 + x) km/hr
Distance = 24 km
As given in the question,
Time for upstream = 1 + Time for downstream
24/(18 - x) = 1 + 24/(18 + x)
24/(18 - x) - 24/(18 + x) = 1
x2 + 48x - 324 = 0
(x + 54)(x - 6) = 0
x ≠ - 54 as speed cannot be negative.
x = 6
The speed of the stream = 6 km/hr