a boat can go 20 km upstream and 30 km downstream in 3 hours. it can go 20 km downstream and 10 km upstream in 1*2/3 hours. find the speed if the boat in still water and the speed of the stream.
Answers
Step-by-step explanation:
Given a boat can go 20 km upstream and 30 km downstream in 3 hours. it can go 20 km downstream and 10 km upstream in 1*2/3 hours. find the speed if the boat in still water and the speed of the stream.
- Let the speed of the boat be m km/hr and speed of the stream be n km/hr.
- So speed upstream will be m – n and speed downstream will be m + n km / hr
- Now speed = distance / time
- So time = distance / speed
- 3 = 20 / m – n + 30 / m + n
- Let 1/m – n = p and 1/m + n = q
- So we have
- 30p + 20 q = 3 -------1
- Also we have
- 1 2/3 = 10 / m -n + 20 / m + n
- 20 p + 10 q = 5/3 ---------2
- Multiply by 2 we get
- 40p + 20 q = 10/3
- So the equations are
- 30p + 20 q = 3
- 40p + 20 q = 10 / 3
- Subtracting we get
- So – 10 p = - 1/3
- Or p = 1/30
- Substituting value of p in 1 we get
- 30 (1/30) + 20 q = 3
- Or 20 q = 3 - 1
- Or q = 2/20
- Or q = 1/10
- Now 1/ m + n = 1/30
- Or m + n = 30
- 1/m – n = 1/10
- Or m – n = 10
- So m + n = 30
- And m – n = 10
- So 2m = 40
- Or m = 20
- Also m + n = 30
- 20 + n = 30
- Or n = 10
- Therefore speed of the boat in still water is 20 km / hr and speed of the stream is 10 km/hr
Reference link will be
https://brainly.in/question/4277614
Given: A boat can go 20 km upstream and 30 km downstream in 3 hours. it can go 20 km downstream and 10 km upstream in 1*2/3 hours.
To find: The speed of the boat in still water and the speed of the stream.
Solution:
- Now we have given boat can go 20 km upstream and 30 km downstream in 3 hours.
- So let the speed of the boat be x and speed of stream be y km/hr
- Then the speed up stream will be: (x-y) km/hr and speed downstream will be ( x +y) km/hr.
- Now we know time = distance / speed
3 = 20/(x-y) + 30/(x+y)
- Consider 1/x-y as a and 1/x-y as b, then:
3 = 20a + 30b ............(i)
- Now we have given it can go 20 km downstream and 10 km upstream in 1*2/3 hours, so:
1 + 2/3 = 10/(x-y) + 20/(x+y)
- Consider 1/x-y as a and 1/x+y as b, then:
5/3 = 10a + 20b .............(ii)
- Now solving (ii)x3 - (i)x2, we get:
5 = 30a + 60b
- 6 = -40a - 60b
-1 = -10a
a = 1/10
- Putting a in (i), we get:
3 = 2 + 30b
b = 1/30
- Now re substituting, we get:
1/(x+y) = b = 1/30
x+y = 30 .......(iii)
1/(x-y) = a = 1/10
x-y = 10 ...........(iv)
- Now solving iii and iv, we get:
2x = 40
x = 20 km/hr
So y = 10 km/hr
Answer:
So the speed of the boat is 20 km/hr and speed of stream is 10 km/hr.