A boat cover 24 km upstream & 28 km downstream in 6 hrs. Also, it covers 30km upstream & 21 km downstream in 6/1/2hrs. find the speed of boat in still water & that of stream.
Answers
Given:
A boat cover 24 km upstream & 28 km downstream in 6 hrs. Also, it covers 30km upstream & 21 km downstream in 6/1/2hrs.
To find:
Find the speed of a boat in still water & that of the stream.
Solution:
Let the speed of boat in still water = x km/hr
Let the speed of stream = y km/hr
Speed in upstream = (x - y) km/hr
Speed in downstream = (x + y) km/hr
Formula: Time = Distance/Speed
Case 1: 24 km upstream & 28 km downstream in 6 hrs
t1 = 24/(x - y)
t2 = 28/(x + y)
t1 + t2 = 6
24/(x - y) + 28/(x + y) = 6
let, 1/(x - y) = A and 1/(x + y) = B
∴ 12A + 14B = 3 ...........(1)
Case 2: 30 km upstream & 21 km downstream in 6 1/2 hrs
t3 = 30/(x - y)
t4 = 21/(x + y)
t3 + t4 = 6 1/2 = 13/2
30/(x - y) + 21/(x + y) = 13/2
let, 1/(x - y) = A and 1/(x + y) = B
∴ 30A + 21B = 13/2 ...........(2)
solving (1) and (2), we get,
A = 1/6 and B = 1/14
⇒ 1/(x - y) = 1/6 and 1/(x + y) = 1/14
⇒ x - y = 6 and x + y = 14
solving the above equations, we get,
x = 10 and y = 4
The speed of boat in still water = x km/hr = 10 km/hr
The speed of stream = y km/hr = 4 km/hr