A boat takes 6 hours to travel 8 km upstream and 32 km downstream and it takes 7 hours to travel 20 km upstream and 16 km downstream. Find the speed of the boat in still water and the speed of the stream.
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Answer:
The speed of boat in still water is 6 km/hr and speed of stream is 2 km/ hr.
Step-by-step explanation:
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.
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Answer:
Step-by-step explanation: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.