) A moto boat required 1 hour to travel 8 kilometers up-stream and 6 kilometers back on a river whose current flow is 3 kms per hour. How fast can the motor boat travel in still water?
Answers
Given:-
- Total time for going upstream and then downstream= 1 hour
- Distance travelled in upstream = 8 km
- Distance travelled in downstream = 6 km
- Speed of river = 3 km/hr
To find:-
- Speed of boat in still water
Formula to be used:-
- Speed = distance/time
→ Time = distance/speed
Answer:-
▪Let the speed of boat in still water be x km/hr.
▪Let the time taken for going upstream be t₁
▪Let the time taken for going downwards be t₂
Upstream:-
‣ Speed of boat = (x - 3) km/hr
‣ Distance = 8 km
‣Time = t₁
So,
⦾ t₁ = 8 / (x - 3) ----( 1 )
Downstream:-
‣ Speed of boat = (x + 3) km/hr
‣ Distance = 6 km
‣ Time = t₂
So,
⦾ t₂ = 6 / (x + 3) ----( 2 )
According to the question, total time taken for going upstream and downstream is 1 hour.
t₁ + t₂ = 1
From ( 1 ) and ( 2 ),
→ [8 / (x - 3)] + [6 / (x + 3)] = 1
→ [8(x + 3) + 6(x - 3)] / [(x - 3)(x + 3)] = 1
Using (a - b)(a + b) = a² - b² in the denominator in L.H.S.,
→ (8x + 24 + 6x - 18) / (x² - 9) = 1
→ 14x + 6 = x² - 9
→ x² - 14x - 15 = 0
Splitting the middle term,
→ x² - 15x + x - 15 = 0
→ x(x - 15) + 1(x - 15) = 0
→ (x - 15)(x + 1) = 0
So,
either x = 15 km/hr
or x = -1 km/hr
Considering only positive value,
→ Speed of boat in still water = x = 15 km/hr Ans.