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
and speed of the boat downstream = (x + y) km/hr
We know that, Time = Distance ÷ Speed
As per the first condition,
8/(x – y) + 32/(x + y) = 6 ....... eq. no. (1)
As per the second condition,
20/(x – y) + 16/(x + y) = 7 ....... eq. no. (2)
Let 1/(x – y) = m and
1/(x + y) = n
∴ Equation
No. (1) will become,
8m + 32n = 6 ...... eq. no. (3)
and Equation Number (2) will become,
20m + 16n = 7 ....... eq. no. (4)
Multiplying equation no. (4) by 2, we get
40m + 32n = 14 ......
eq. no. (5)
Subtracting equation (3) from equation (5)
|
40m + 32n = 14
|
|
8m + 32n = 6
|
|
(-) (-) (-)
|
|
32m = 8
|
∴ m
= 8/32
∴ m
= ¼
Substituting m = ¼ in
equation number (3)
∴ 8m
+ 32n = 6
∴ 8(¼)
+ 32n = 6
∴ 2
+ 32n = 6
∴ 32n
= 6 – 2
∴ 32n
= 4
∴ n
= 4/32
∴ n
= 1/8
Resubstituting the values of m and n we get,
|
m = 1/(x – y)
∴ ¼
= 1/(x – y)
∴ x
– y = 4...... eq. no. (A)
|
n = 1/(x + y)
∴ 1/8
= 1/(x + y)
∴ x
+ y = 8 ....... eq. no. (B)
|
Adding equations (A) and (B) ,
|
x – y = 4
|
|
x + y = 8
|
|
2x = 12
|
∴ x
= 12/2
∴ x
= 6
Substituting x = 6 in equation (B),
∴ x
+ y = 8
∴ 6
+ y = 8
∴ y
= 8 – 6
∴ y
= 2
∴ The speed of boat in still
water is 6 km/hr and speed of stream is 2
km/ hr.