Advertisements
Advertisements
Question
A boat goes 18 km upstream in 3 hours and 24 km downstream in 2 hours. Find the speed of the boat in still water and the speed of the stream.
Advertisements
Solution
Let the speed of the boat in still water be x km/hr
and the speed of the stream be y km/hr.
Speed of the boat upstream = (x - y)km/hr.
Speed of the boat downstream = (x + y)km/hr
Time required to go 18 km upstream = 3 hours
⇒ `(18)/(x - y)` = 3
⇒ `(6)/(x - y)` = 1
⇒ x - y = 6 ....(i)
Time required to go 24 km downstream = 2 hours
⇒`(24)/(x + y)` = 2
⇒ `(12)/(x + y)` = 1
⇒ x + y = 12 ....(ii)
Adding eqns. (i) and (ii), we get
2x = 18
⇒ x = 9
⇒ 9 - y = 6
⇒ y = 3
Thus, the speed of the boat in still water is 9 km/hr and the speed of the stream is 3km/hr.
APPEARS IN
RELATED QUESTIONS
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
`[ x - y ]/6 = 2( 4 - x )`
2x + y = 3( x - 4 )
Solve the following simultaneous equations :
2(3u - v) = 5uv
2(u + 3v) = 5uv
Solve the following simultaneous equations:
13a - 11b = 70
11a - 13b = 74
Solve the following simultaneous equations:
103a + 51b = 617
97a + 49b = 583
Solve the following pairs of equations:
`(2)/x + (3)/y = (9)/(xy)`
`(4)/x + (9)/y = (21)/(xy)`
Where x ≠ 0, y ≠ 0
Solve the following pairs of equations:
`(5)/(x + y) - (2)/(x - y)` = -1
`(15)/(x + y) + (7)/(x - y)` = 10.
If 2x + y = 23 and 4x - y = 19 : find the value of x - 3y and 5y - 2x.
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes `(1)/(2)`. Find the fraction.
Salman and Kirti start at the same time from two places 28 km apart. If they walk in the same direction, Salman overtakes Kirti in 28 hours but if they walk in the opposite directions, they meet in 4 hours. Find their speeds (in km/h).
A and B can build a wall in `6(2)/(3)` days. If A's one day work is `1(1)/(4)` of one day work of B, find in 4 how many days A and B alone can build the wall.
