A boat takes 5 hours to travel 12 km downstream and 16 km upstream, and it takes 7
hours to travel 16 km downstream and 24 km upstream. Find the speed of the boat in still
water and the speed of the stream.
Answers
Answer:
Let speed of boat be x and stream be y
Speed of boat in upstream = x-y
Speed of boat in downstream = x+y...............due to gravity.
time= dist/speed.
According to 1st condition;
12/x+y + 16/x-y = 5
According to 2nd condition;
16/x+y + 24/x-y = 7
Substitute 1/x+y = a and 1/x-y = b
12a + 16b = 5...............1
16a + 24b = 7................2
multiply eq 1 by 4 and eq 2 by 3
48a + 64b = 20..................3
48a + 72b = 21....................4
Substract eq 3 from 4
48a + 72b = 21
- 48a + 64b = 20
(-) (-) (-)
8b = 1 .............................eliminating 48a
b = 1/8
substitute b = 1/8 in eq 1
12a + 16 (1/8) = 5
12a + 2 = 5
12a = 5-2
12a = 3
a = 3/12
a = 1/4
Resubstitute a = 1/x+y and b = 1/ x-y
x+y=4 and x-y=8........................Both are DENOMINATORS
Add x+y = 4 and x-y = 8
x+y=4
x-y=8
2x = 12
x = 6
Substitute x = 6 in x+y= 4
6 + y = 4
y = 4-6
y = -2
Therefore,
Speed of boat is 6km/hr and
Speed of stream is -2km/hr.
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