pls answet it and i will mark u brainliest. A motorboat goes downstream in the river and covers the distance between two coastal town in 3 hours. It covers this distance upstream in 4 hours.Given the speed of the stream is 5 km/hr.
Speed of the stream is the getting added or subtracted to the speed of boat while travelling in the same direction or opposite direction respectively.
69The speed of the boat in still water is
(options:-
A. 28 km/hr
B. 34 km/hr
C. 25 km/hr
D. 35 km/hr
2. The distance between the two coastal towns is
(1 Point)
A. 120 km
B. 116 km
C. 100 km
D. 92 km
Answers
SOLUTION :-
Let the speed of boat in still water be x.
Downstream :-
Speed of boat = ( x + 5 ) km/h
Time taken = 3 hours
Distance while going downstream = Speed × Time
= 3 ( x + 5 ) Km
Upstream :-
Speed of boat = ( x - 5 ) km/h
Time taken = 4 hours
Distance while going upstream = Speed × Time
= 4 ( x - 5 ) km
According to the question,
Speed of boat in still water = 35 km/h
Option D is correct
____________________________________
Distance = Speed × Time
Distance while going downstream = 3 ( 35 + 5 )
= 3 × 40
= 120 km
Distance while going upstream = 4 ( 35 - 5 )
= 4 × 30
= 120 km
Hence distance = 120 km
Option A is correct.
Answer :-
▶ Speed of the boat in still water = Option D = 35 Km/hr
▶The distance between the two coastal towns is = Option A = 120 Km/hr
★ Concept :-
Here the concept of Linear Equation in One Variable is used where by getting the value of other variable we find another using algebraic method.
Also,
• When the body is going downstream, the speed of body is added to the speed of stream.
• When the body is going upstream, the speed of stream is subtracted from the speed of the body.
• Distance = Speed × Time
★ Solution :-
✏ Let the speed of the boat be 'x' Km/hr.
Then,
Speed of the stream = 5 km / hr (given)
▶For distance covered by boat in Downstream :
Given,
• Time taken for the journey = 3 hours
• Speed of the boat = (x + 5) Km/hr
We know that,
• Distance = 3 × (x + 5) Km ...(i)
▶ For distance covered by boat in Upstream :
Given,
• Time taken for the journey = 4 hours
• Speed of the boat = (x - 5) Km/hr
We know that,
• Distance = 4 × (x - 5) Km ...(ii)
Also, we know that
• Distance covered in upstream = Distance Covered in downstream ,
Because the distance between coastal towns is equal.
So equating both equations of (i) and (ii) , we get,
✒ 3 × (x + 5) = 4 × (x - 5)
✒ 3x + 15 = 4x - 20
By transposing like terms other side, we get,
✒ 15 + 20 = 4x - 3x
✒ x = 35
* Hence, we get, the speed of boat in still water = 35 Km / hr
» Now distance between two coastal towns, is given by, by taking here the distance covered in downstream,
✒ Distance = Speed × Time
✒ Distance = (x + 5) × 3
✒ Distance = (35 + 5) × 3
✒ Distance = 40 × 3 = 120 Km
* Hence, the distance between two coastal towns = 120 Km
So, for the speed of boat in still water option D) is correct.
And for the distance between two coastal towns option A) is correct.
★ More to know :-
• While travelling in downstream, the speed of boat is increased by the sum of its speed and speed of stream travelling along with it. That is why, speed of stream is added in this case.
• While travelling in upstream, the speed of boat is decreased by the difference of its speed and speed of stream travelling opposite with it. That is why, speed of stream is subtracted here.
• Linear equation shows best determines the Trial and Error method, where when drawing a graph, and by applying values, we get correct value. But here we have used algebraic method which is easier to get our answer.