A motorboat goes downstream in a rivercan cover the distance between two coastal towns in 5 hours a it covers the distance upstream in 6 hours if the speed of the stream is 2 kilometre per hour find the speed of the boat in still water
Answers
AnswEr :
Let the Speed of Boat in still water be x Km/hr and, Speed of Stream be y Km/hr.
• G I V E N :
Time taken in Upstream is 6 hours, whereas Time taken in Downstream is 5 hours. Speed of Stream is 2 km/hr
Distance Travelled is Fixed Here.
◗ Upstream = (x - y) = (x - 2) km/hr
◗ Downstream = (x + y) = (x + 2) km/hr
• Let's Head to the Question Now :
⇒ Distance⁽ᵘᵖˢᵗʳᵉᵃᵐ⁾ = Distance⁽ᵈᵒʷⁿˢᵗʳᵉᵃᵐ⁾
⇒ Upstream × Time = Downstream × Time
⇒ (x - 2) km/hr × 6 hr = (x + 2) km/hr × 5 hr
⇒ 6x - 12 = 5x + 10
⇒ 6x - 5x = 10 + 12
⇒ x = 22 km/hr
∴ Speed of Boat in Still water is 22 km/hr
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• V E R I F I C A T I O N :
↠ Distance⁽ᵘᵖˢᵗʳᵉᵃᵐ⁾ = Distance⁽ᵈᵒʷⁿˢᵗʳᵉᵃᵐ⁾
↠ Upstream × Time = Downstream × Time
↠ (x - 2) × 6 = (x + 2) × 5
↠ (22 - 2) × 6 = (22 + 2) × 5
↠ 20 × 6 = 24 × 5
↠ 120 Km = 120 Km ⠀⠀Hence, Verified!
Answer:
Step-by-step explanation:
Given :-
Speed of the stream = 2 km/h.
To Find :-
Speed of the boat in still water.
Formula to be used :-
Distance = Speed x Time
Solution :-
Let the speed of the boat in still water be x.
As per the Question,
Upstream :-
Speed = ( x - 2) km/h
Distance = Speed x Time
Distance = 6 (x - 2) km
Downstream :-
Speed = ( x + 2) km/h
Distance = Speed x Time
Distance = 5(x + 2) km
As per the Question,
⇒ 6(x- 2) = 5( x + 2)
⇒ 6x - 12 = 5x + 10
⇒ x = 22 km/h
Hence, The speed of the boat in still water is 22 km/h.