A boat goes 24km/hr upstream and 28km/hr downstream in 6hrs. In 6 whole 1/2 ,it can go 30km upstream and 21km downstream. Determine the speed of the stream and that of the boat in still water.
Answers
Answer:
Let the speed of boat be x in still water and stream be y.
Speed of boat in downstream = x+y. (because of gravity)
speed of boat in upstream = x-y
time=dist/speed
According to 1st condition;
24/x-y + 28/x+y = 6...........................1
According to 2nd condition;
30/x-y + 21/x+y = 6×1/2
30/x-y + 21/x+y = 13/2.......................2
Substituting 1/x-y = a and 1/x+y = b
therefore, 24a + 28b = 6................3
and, 30a + 21b = 13/2...................4
divide eq 3 by 2.
12a + 14b = 3................5
multiply eq 4 by 2.
60a + 42b =13..............6
multiply eq 5 by 5.
60a + 70b = 15...............7
Substract eq 6 from 7
60a + 70b = 15
- 60a + 42b = 13
(-) (-) (-) { changing the signs }
therefore, 28b = 2......................{ eliminating 60a }
b = 2/28
therefore, b= 1/14
substitute b=1/14 in eq 5..............(you can prefrr any of them)
12a + 14(1/14) = 3
12a + 1 = 3
12a = 3-1
12a = 2
a =2/12
a = 1/6
Resubstitute 1/x-y = a and 1/x+y = b
therefore;
x-y = 6 and x+y = 14..................( Both are DENOMINATORS )
Add x-y = 6 and x+y = 14
x-y = 6
+x+y = 14
2x = 20
x = 20/2 = 10
x= 10
substitute x=10 in x-y = 6
10-y = 6
-y = 6 - 10
-y = -4
y = 4
Therefore,
The speed of boat is 10km/hr and stream is 4km/hr.
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