A boat covers the distance of 300 km going upstream in 15 hours. In return journey, covers the same distance in 10 hours. How much time will the boat take to cover the distance of 400 kilometres in still water?
Answers
Let :
- Speed of boat in still water = v₁ km/h
- Speed of stream = v₂ km/h
Given :
- Boat covers 300km upstream in 15hours
- Boat covers 300km downstream in 10hours
To find :
Time taken by boat to cover 400km in still water
Formula used :
Distance = speed × time
Steps to follow :
- First of all find relationship between v₁ & v₂.
- Find Value of v₁ & v₂ , by solving linear equations formed
- Find required time taken
Solution :
Upstream -
Relative speed of boat upstream = Speed of boat in still water - speed of stream
Relative speed of boat upstream = v₁ - v₂
➝ Time = 15 hours
➝ Distance = 300km
Distance = speed × time
➝ 300km = 15 hr × (v₁ - v₂)
➝ (v₁ - v₂) = 300 ÷ 15
➝ (v₁ - v₂) = 20
➝ v₁ = v₂ + 20...... equation 1
_______________________________________________
Downstream -
Relative speed of boat downstream = Speed of boat in still water + speed of stream
Relative speed of boat downstream = v₁ + v₂
➝ Time = 10 hours
➝ Distance = 300km
Distance = speed × time
➝ 300km = 10 hr × (v₁ + v₂)
➝ (v₁ + v₂) = 300 ÷ 10
➝ (v₁ + v₂) = 30 ...... equation 2
_______________________________________________
On putting value of v₁ , from equation 1 into equation 2, we get;
➝ ( v₂ + 20) + v₂ = 30
➝ 2v₂ = 30 - 20
➝ 2v₂ = 10
➝ v₂ = 10 ÷ 2
➝ v₂ = 5
_______________________________________________
On putting value of v₂ in equation 1 , we get;
➝ v₁ = 5 + 20
➝ v₁ = 25
This gives, speed of boat in still water = 25km/h
_______________________________________________
Still water -
Distance = 400km
Speed of boat in still water = 25km/h
Time taken = Distance ÷ speed
➝ Time taken = 400km ÷ 25km/h
➝ Time taken = 16 hours
_______________________________________________
ANSWER :
Time taken by boat to cover 400km in still water = 16 hours