Question

The ratio of speed of the boat to that of the
current is 7:3. If the boat goes downstream
in 6 hrs 20 minutes, then it will return in-​

Answer 1

Given :-

• Ratio of speed of the boat to that of the
• current is 7:3.
• Downstream Time = 6 hours 20 min.

To Find :-

• How much Time The boat will take in return ?

Formula used :-

• Downstream speed = (Speed of boat in still water + Speed of current ).
• Upstream Speed = (Speed of boat in still water - Speed of current ).
• Time = Distance / Speed .
• 60 minutes = 1 hour.

Solution :-

we Have :-

→ Let speed of boat in still water = 7x km/h.

→ Let speed of current = 3x km/h.

→ So, Downstream Speed = 7x + 3x = 10x km/h.

→ Let Distance covered = D km.

→ Time = 6 hours + 20 min . = 6 + (20/60) = 6(1/3) = (19/3) hours.

So, we can say That,

→ D = S * T

→ D = (10x) * (19/3)

→ D = (190x/3) km .

Now, we Have to come back to initial Position , That Means we have to come in upstream.

So,

→ Upstream speed = (7x - 3x) = 4x km/h.

So,

→ Time = Distance / Speed .

→ Time = { (190x/3) / 4x }

→ Time = (190/12)

→ Time = 15 + (10/12) = 15 + (10/12 * 60) = 15 hours + 50 minutes.

Hence , The boat will take 15 hours , 50 minutes in Return.

Answer 2

Answer:

Let Speed of Boat & Current be 7n & 3n.

• Downstream = (7n + 3n) = 10n
• Upstream = (7n – 3n) = 4n

$\underline{\bigstar\:\:\textsf{As the Distance is Constant Here :}}$

$:\implies\tt Speed_{Downstream} \times Time=Speed_{Upstream} \times Time\\\\\\:\implies\tt 10n \times 6 \:hr. \:20 \:min.=4n \times Time\\\\\\:\implies\tt 10n \times(6 \times 60 + 20) \:min.=4n \times Time\\\\\\:\implies\tt 10n \times (360 + 20) \:min. = 4n \times Time\\\\\\:\implies\tt 10n \times 380 \:min. = 4n \times Time\\\\\\:\implies\tt \dfrac{10n \times 380 \:min.}{4n} =Time\\\\\\:\implies\tt Time =5 \times 190 \:min.\\\\\\:\implies\tt Time = 950 \:min.\\\\{\scriptsize\qquad\bf{\dag}\:\:\textsf{Changing it into Hour.}}\\\\:\implies\tt Time = \dfrac{950}{60} \:hr.\\\\\\:\implies\underline{\boxed{\textsf{\textbf{Time = 15hr. \:50min.}}}}$

⠀

$\therefore\:\underline{\textsf{It will take \textbf{15hr. 50min.} in returning upstream}}.$