Correct Answer - Option 4 :
\(1 \frac{1}{5}\)h
Given:
The speed of the boat in still water is 4 times the speed of the stream
Boat travel a distance in upstream and downstream = 45 km
Formula:
Speed of boat in downstream = Speed of a boat in still water + Speed of a boat in the stream
Speed of boat in upstream = Speed of a boat in still water + Speed of a boat in the stream
Speed = Distance/Time
Calculation:
Let the speed of the boat in still water be x km/h and speed of the boat in-stream be y km/h
When boat travel in downstream took time = t hour
When boat travel in upstream too time = (t + 0.5) hour
Boat travel a distance in upstream and downstream = 45 km
The ratio of speed of the boat in still water and speed of the boat in-stream = 4x ∶ x
Speed of boat in downstream = x + y
Speed of boat in upstream = x – y
Now,
We know that –
Distance = speed × time
Now,
In downstream,
45 = (4x + x) × t ……… (1)
In upstream,
45 = (4x – x) × (t + 0.5) ……. (2)
Now,
Equate the equation (1) & (2) then we get,
5x × t = 3x × (t + 0.5)
⇒ 5tx = 3tx + 1.5x
⇒ 5tx – 3tx = 1.5x
⇒ 2tx = 1.5x
⇒ 2t = 1.5
⇒ t = 1.5/2
⇒ t = 0.75
Now,
Put the value of t = 0.75 in equation (1) then we get
45 = (4x + x) × 0.75
⇒ 45 = 5x × 0.75
⇒ 45 = 3.75x
⇒ x = 45/3.75
⇒ x = 4500/375
⇒ x = 900/75
⇒ x = 180/15
⇒ x = 36/3
⇒ x = 12
Now,
Speed of boat in still water = 4x
⇒ 4 × 12
⇒ 48 km/h
Speed of boat in stream = x
⇒ 12 km/h
Speed of boat in downstream = 48 + 12
⇒ 60 km/h
Distance cover by boat in downstream = 72 km
Now,
We know that –
Time = distance/speed
⇒ 72/60
⇒ 6/5
⇒\(1 \frac{1}{5}\)
∴ The boat will take a time to cover a distance of 72 km is \(1 \frac{1}{5}\) hour
