Question

hey guys need help for this problem

Answer 1

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.