A boat travelled at a constant speed of 3 miles per hour in still water (a part of a stream where no
current is visible). However, it took twice as long to travel 60 miles upstream (against the current) than
it takes for the 60 mile return trip (with the current). What is the speed of the current in the river? SHOW ME YOUR SOLUTION
Answers
Answer:
sorry I didn't know the answer
Answer:
1 m/h
Step-by-step explanation:
Let the speed of the stream constant and be x
Given:
Speed of the boat = 3m/h
Distance travelled in upstream (d₁) = 60miles
Speed of boat in upstream (v₁) = (3 - x) m/h
Distance travelled in downstream (d₂) = 60miles
Speed of boat in downstream (v₂) = (3 + x) m/h
Now,
Time is taken in upstream (t₁) = d₁/v₁
= 60/ (3 - x)................................(i)
Time is taken in downstream (t₂) = d₂/v₂ = 60/(3 + x).........................(ii)
As we know, that the time taken to travel upstream is twice the time travel in downstream if the speed of the stream is constant
∴ t₁ = 2t₂
Substituting the values from the equation (i) and (ii)
60/(3 - x) = 2 × 60/(3 + x)
⇒ 60/(3 - x) = 120/(3 + x)
⇒ 60 (3 + x) = 120 (3 - x)
⇒ 180 + 60x = 360 - 120x
⇒ 120x + 60x = 360 - 180
⇒ 180x = 180
⇒ x = 180/180
⇒ x = 1m/h