Maths

66 MATHEMATICS
t
2
Let t 2
be the time, in hours, taken by the boat to go 44 km downstream. Then
44 . The total time taken, t 1
+ t 2
, is 10 hours. Therefore, we get the equation
x y
✁
30 44
= 10 ✁
(1)
✂
✁ x y x y
In the second case, in 13 hours it can go 40 km upstream and 55 km downstream. We
get the equation
Put
40 55
✁
x y x y
1 1
u and
x y x y
✂
✂
✁
✁
= 13 (2)
v
On substituting these values in Equations (1) and (2), we get the pair of linear
equations:
30u + 44v = 10 or 30u + 44v – 10 = 0 (4)
40u + 55v = 13 or 40u + 55v – 13 = 0 (5)
Using Cross-multiplication method, we get
u
v
1
=
44( 13) 55( 10) 40( 10) 30( 13) 30(55) 44(40)
u v 1
i.e.,
☎ =
22 ✄ ✄ 10 ✄
110
i.e., u = 1 , v = 1
5 11
Now put these values of u and v in Equations (3), we get
✂ ✂ ✂
✂ ✂ ✂ ✂
✂
✁
1 1 1 1
and
x y 5 x y 11
i.e., x – y = 5 and x + y = 11 (6)
Adding these equations, we get
2x =16
i.e., x =8
Subtracting the equations in (6), we get
2y =6
i.e., y =3
(3)