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 :
13 + 2y = 9x
3y = 7x
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
`[5y]/2 - x/3 = 8`
`y/2 + [5x]/3 = 12`
For solving pair of equation, in this exercise use the method of elimination by equating coefficients:
y = 2x - 6; y = 0
Solve :
11(x - 5) + 10(y - 2) + 54 = 0
7(2x - 1) + 9(3y - 1) = 25
Solve the following simultaneous equations:
13a - 11b = 70
11a - 13b = 74
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:
`(2)/(x + 1) - (1)/(y - 1) = (1)/(2)`
`(1)/(x + 1) + (2)/(y - 1) = (5)/(2)`
Solve the following pairs of equations:
`(2)/(3x + 2y) + (3)/(3x - 2y) = (17)/(5)`
`(5)/(3x + 2y) + (1)/(3x - 2y)` = 2
Seven more than a 2-digit number is equal to two less than the number obtained by reversing the digits. The sum of the digits is 5. Find the number.
In a triangle, the sum of two angles is equal to the third angle. If the difference between these two angles is 20°, determine all the angles.
