Q10. A boat went downstream for 160 km and returned immediately. It took the boat 20 hr. to complete the round trip. If the speed of the river were twice as high, the trip to downstream and back would take 32 hours. What is the speed of boat in still water? A. 15 km/hour B. 16 km/hour C. 14 km/hour D. 18 km/hour
Answers
Step-by-step explanation:
16km/hr is the answer
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- The speed of boat in still water is 18 km/h .
Given :- A boat went downstream for 160 km and returned immediately. It took the boat 20 hr. to complete the round trip. If the speed of the river were twice as high, the trip to downstream and back would take 32 hours.
To Find :- The speed of boat in still water ?
Formula used :-
- Downstream speed = Speed of boat in still water + Speed of current .
- Upstream speed = Speed of boat in still water - Speed of current .
- Distance = Speed × Time .
Solution :-
Let speed of boat in still water is x km/h and speed of stream is y km/h .
First case :- Distance covered is 160 km , speed of current is y km/h and total time for round trip is 20 hours .
So,
→ 160/(x + y) + 160/(x - y) = 20
→ (x - y + x + y)/(x² - y²) = 20/160
→ 2x/(x² - y²) = 1/8
→ 16x = x² - y²
→ x² = (16x + y²) ------ (1)
Second case :- Distance covered is 160 km, speed of current is 2y km/h and total time for round trip is 32 hours .
→ 160/(x + 2y) + 160/(x - 2y) = 32
→ (x - 2y + x + 2y)/(x² - 4y²) = 1/5
→ 10x = x² - 4y²
→ x² = 10x + 4y² ------ (2)
from (1) and (2) :-
→ 16x + y² = 10x + 4y²
→ 6x = 3y²
→ 2x = y² ------ (3)
putting (3) in (2) :-
→ x² = 10x + 4(2x)
→ x² = 18x
→ x = 18 km/h (Ans.)
Hence, the speed of boat in still water is equal to 18 km/h .
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