i) A boat takes 6 hours to travel 36 km downstream and 24 km upstream. It takes 9 hours to travel 48 km downstream and 40 km upstream. Find the speed of the stream and that of boat in still water.... if the answer is right i will mark you as brainliest
Answers
Step-by-step explanation:
Let's say that the speed of boat in still water is x km/hr and of stream is y km/hr.
Now,
Downstream speed of boat is (x + y) km/hr and upstream speed of boeat is (x - y) km/hr.
Time = Distance/Speed
As per question, boat takes 6 hours to travel 36 km downstream and 24 km upstream.
→ 36/(x + y) + 24/(x - y) = 6
Let's say 1/(x + y) is a and 1/(x - y) is b.
→ 36a + 24b = 6 ---------- (eq 1)
Similarly, it takes 9 hours to travel 48 km downstream and 40 km upstream.
→ 48/(x + y) + 40/(x - y) = 9
→ 48a + 40b = 9 --------- (eq 2)
On multiplying (eq 1) with 5 and (eq 2) with 3 we get,
→ 180a + 120b = 30
→ 120b = 30 - 180a --------- (eq 3)
→ 144a + 120b = 27
→ 120b = 27 - 144a --------- (eq 4)
On comparing (eq 3) & (eq 4) we get,
→ 30 - 180a = 27 - 144a
→ 30 - 27 = - 144a + 180a
→ 3 = 36a
→ a = 1/12
Substitute value of a in (eq 3)
→ 120b = 30 - 180 × 1/12
→ 120b = 30 - 15
→ b = 15/120
→ b = 1/8
Now,
→ 1/(x + y) = a = 1/12
→ x + y = 12
→ x = 12 - y -------- (eq 5)
→ 1/(x - y) = b = 1/8
→ x - y = 8
→ x = 8 + y -------- (eq 6)
On comparing (eq 5) & (eq 6) we get,
→ 12 - y = 8 + y
→ 4 = 2y
→ y = 2
Substitute value of y in (eq 5)
→ x = 12 - 2
→ x = 10
Therefore, the speed of the stream is 2 km/hr and that of boat in still water is 10 km/hr.