A motorboat whose speed is 18km/hr in still water take 1 hr more to go 24km upstream than to return downstream to the same spot. Find the speed of the stream.
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A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
The question is a real-life application of linear equations in two variables.
Answer: The speed of the stream is 6 km/hr.
Let's explore the water currents.
Explanation:
Let the speed of the stream be x km/hr
Given that, the speed boat in still water is 18 km/hr.
Sspeed of the boat in upstream = (18 - x) km/hr
Speed of the boat in downstream = (18 + x) km/hr
It is mentioned that the boat takes 1 hour more to go 24 km upstream than to return downstream to the same spot
Therefore, One-way Distance traveled by boat (d) = 24 km
Hence, Time in hour
Tupstream = Tdownstream + 1
[distance / upstream speed ] = [distance / downstream speed] + 1
[ 24/ (18 - x) ] = [ 24/ (18 + x) ] + 1
[ 24/ (18 - x) - 24/ (18 + x) ] = 1
24 [1/ (18 - x) - 1/(18 + x) ] = 1
24 [ {18 + x - (18 - x) } / {324 - x2} ] = 1
24 [ {18 + x - 18 + x) } / {324 - x2} ] = 1
⇒ 24 [ {2}x / {324 - x2} ] = 1
⇒ 48x = 324 - x2
⇒ x2 + 48x - 324 = 0
⇒ x2 + 54x - 6x - 324 = 0 ----------> (by splitting the middle-term)
⇒ x(x + 54) - 6(x + 54) = 0
⇒ (x + 54)(x - 6) = 0
⇒ x = -54 or 6
As speed to stream can never be negative, we consider the speed of the stream (x) as 6 km/hr.
Step-by-step explanation:
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Answer:
A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
The question is a real-life application of linear equations in two variables.
Answer: The speed of the stream is 6 km/hr.
Let's explore the water currents.
Explanation:
Let the speed of the stream be x km/hr
Given that, the speed boat in still water is 18 km/hr.
Sspeed of the boat in upstream = (18 - x) km/hr
Speed of the boat in downstream = (18 + x) km/hr
It is mentioned that the boat takes 1 hour more to go 24 km upstream than to return downstream to the same spot
Therefore, One-way Distance traveled by boat (d) = 24 km
Hence, Time in hour
Tupstream = Tdownstream + 1
[distance / upstream speed ] = [distance / downstream speed] + 1
[ 24/ (18 - x) ] = [ 24/ (18 + x) ] + 1
[ 24/ (18 - x) - 24/ (18 + x) ] = 1
24 [1/ (18 - x) - 1/(18 + x) ] = 1
24 [ {18 + x - (18 - x) } / {324 - x2} ] = 1
24 [ {18 + x - 18 + x) } / {324 - x2} ] = 1
⇒ 24 [ {2}x / {324 - x2} ] = 1
⇒ 48x = 324 - x2
⇒ x2 + 48x - 324 = 0
⇒ x2 + 54x - 6x - 324 = 0 ----------> (by splitting the middle-term)
⇒ x(x + 54) - 6(x + 54) = 0
⇒ (x + 54)(x - 6) = 0
⇒ x = -54 or 6
As speed to stream can never be negative, we consider the speed of the stream (x) as 6 km/hr.
Thus, the speed of the stream is 6 km/hr.