Q3) A boat takes 9 hours to travel 30 km upstream and 40 km downstream but it takes 12 hours to travel 42 km upstream and 50 km downstream. Find the speed of the boat in still water and the speed of the stream
Answers
Answer:
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Step-by-step explanation:
Let the distance covered by the boat each way be d km. And let the velocity of the stream be v km/hr.
While going downstream the velocity of the boat is (v+4) km/hr.
While going upstream the velocity of the boat is (v-4) km/hr.
d/(v+4) = 3, or
d = 3v +12 …(1)
d/(v-4) = 9, or
d = 9v - 36 …(2).
Equating (1) and (2)
d = 3v +12 = 9v - 36, or
9v-3v = 6v = 12+36 = 48, or
v = 48/6 = 8 km/hr
The velocity of the stream is 8 km/hr. The distance covered, d = 36 km.
Check: While going downstream time taken = 36/(4+8) = 3 hours. Correct.
While going upstream time taken = 36/(8–4) = 9 hours. Correct.
SOLUTION ::
Let the speed of the boat in still water = x km/h
The speed of the stream = y km/h
We know that
Total time = Upstream distance/upstream speed + Downstream dist/downstream speed
Upstream speed
= speed of boat - speed of stream
= x - y
Down stream speed = x + y
BY THE GIVEN CONDITION
30/x-y + 40/x+y = 9 ............. (i)
42/x-y + 50/x+y = 12 .............(ii)
Multiplying eq.(i) by 5 & eq.(ii) by 4
150/x-y + 200/x+y = 45 ......(iii)
168/x-y + 200/x+y = 48 ......(iv)
Now (iii) - (iv) gives
-18/x-y = - 3
x-y = 6 .....(v)
Substituting (v) in (iii)
150/x-y + 200/x+y = 45
150/6 + 200/x+y = 45
200/x+y = 20
x + y = 10........(vi)
Adding (v) & (vi) We get
2x = 16
x = 8
8+y = 10
y= 2
Hence speed of boat = 8 km/h
Speed of stream = 2 km/h