Question

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Answer 1

Let speed of the boat in still water = x
Let speed of steam = y
Speed of boar to go downstream = x + y
Speed of the boat to go upstream = x - y
Time taken by boat to go 24km upstream
= 24/(x - y)
Time taken by boat to go 28 km downstream
= 28/ (x + y)
Total time taken = 6hrs
24/(x - y) + 28/(x + y) = 6
Time taken by boat to go 30km upstream
= 30/(x - y)
Time taken by boat to go 21 km downstream
= 21/ (x + y)
Total time taken = 6.5hrs
= 6 ½
30/(x - y) + 21/(x + y) = 6½
Let 1/(x - y) = a
1/(x + y) =b
24a + 28b = 6
12a + 14b = 3...........eq1
30a + 21b = 13/2.......eq2
Eq 1 * 5 = 60a + 70b = 15
Eq 2 * 2 = 60a + 42b = 13
- - -
_____________________
28b = 2
b = 2/28
= 1/14
From Eq 1........ 12a + 14*1/14 = 3
12a = 2
a =1/6
1/(x - y) = 1/6
x - y = 6
1/(x + y) = 1/14
x + y = 14

x - y = 6
x + y = 14
________
2x = 20
x = 10
10 - y = 6
y = 4
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