A boat can travel 6 km downstream in 40 minutes. The return trip requires an hour. Find the rate of the boat in still water and the rate of the current.
Answers
||✪✪ QUESTION ✪✪||
A boat can travel 6 km downstream in 40 minutes. The return trip requires an hour. Find the rate of the boat in still water and the rate of the current. ?
|| ★★ CONCEPT USED ★★ ||
if Speed of boat in x km/h , and speed of current is y km/h , Than :-
→ Speed in Downstream = (x + y) km/h .
→ Speed in Upstream = (x - y) km/h.
Also , Time = (Distance / Speed ) .
→ 1 hour = 60 Minutes .
|| ✰✰ ANSWER ✰✰ ||
Let us assume That Speed of boat in Still water is x km/h , and speed of current is y km/h .
So, we can say That :-
→ 6/(x + y) = 40 min . = 40/60 = (2/3) hours.
Cross - Multiply,
→ 2(x + y) = 6*3
→ (x + y) = 9 ------------ Equation (1).
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Also,
→ 6/(x - y) = 1
→ (x - y) = 6 . ------------ Equation (2).
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Adding both Equations We get,
→ (x + y) + (x - y) = 9 + 6
→ 2x = 15
Dividing both sides by 2
→ x = 7.5km/h.
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Putting This value in Equation (1) we get,
→ 7.5 + y = 9
→ y = 9 - 7.5
→ y = 1.5km/h.
Hence, Speed of the boat in still water is 7.5km/h and the rate of the current is 1.5km/h.
Given: A boat can travel 6 km downstream in 40 minutes and return back upstream in an hor [60 minutes].
To find: The speed of the boat and the current.
Answer:
Let the speed of the boat be x km/h and that of the current be y km/.
This implies that:
- x + y = [downstream]
- x - y = [upstream]
We know that speed = .
Therefore, according to the question,
Equation 1 ⇒ x - y = 6.
Equation 2 ⇒ x + y = 2x + 2y = 18 ⇒ x + y = 9.
On solving the equations, we get x = 7.5 and y = 1.5.
Therefore, the speed of the boat in still water is 7.5 km/h and speed of the current is 1.5 km/h.