In still water a boat takes total 15 hours to go to destination & then come back to the initial position. If there is a flow in the river then the boat takes 16 hours in the same journey. Difference of speeds of boat & stream is 15 km/hr. What is the speed of stream?
Answers
- The speed of stream is equal to 5 km/h .
Given :- In still water a boat takes total 15 hours to go to destination & then come back to the initial position. If there is a flow in the river then the boat takes 16 hours in the same journey. Difference of speeds of boat & stream is 15 km/hr.
To Find :-
- The speed of stream ?
Formula used :-
- Distance = Speed × Time
- Time = Distance ÷ Speed
- Downstream speed = speed of boat in still water + speed of stream .
- Upstream speed = speed of boat in still water - speed of stream .
Solution :-
Let us assume that, speed of boat in still water is x km/h and speed of stream is y km/h .
So,
→ Downstream speed = (x + y) km/h
→ Upstream speed = (x - y) km/h
Also, it is given that,
→ x - y = 15 km/h --- Eqn.(1)
Now,
→ Distance covered in one way = Speed in still water × Time taken in one way = x * 7.5 = 7.5x km
A/q,
→ {7.5x/(x + y)} + {7.5x/(x - y)} = 16
putting value of Eqn.(1)
→ {7.5x/(x + y)} + {7.5x/15} = 16
→ {7.5x/(x + y)} + 0.5x = 16
→ (7.5x + 0.5x² + 0.5xy) = 16x + 16y
→ 0.5x² + 0.5xy = 16x - 7.5x + 16y
→ 0.5x² + 0.5xy = 8.5x + 16y
→ 0.5(x² + xy) = 8.5x + 16y
→ x² + xy = 17x + 32y
again, putting value of y from Eqn.(1),
→ x² + x(x - 15) = 17x + 32(x - 15)
→ x² + x² - 15x = 17x + 32x - 480
→ 2x² - 15x - 49x + 480 = 0
→ 2x² - 64x + 480 = 0
→ 2(x² - 32x + 240) = 0
→ x² - 32x + 240 = 0
→ x² - 20x - 12x + 240 = 0
→ x(x - 20) - 12(x - 20) = 0
→ (x - 20)(x - 12) = 0
putting both equal to zero we get,
→ x = 20 km/h and 12 km/h
since, (x - y) is equal to 15 km/h, value x can't be 12km/h .
Therefore,
→ x = 20 km/h
hence,
→ y = (x - 15)
→ y = 20 - 15
→ y = 5 km/h
∴ The speed of stream is equal to 5 km/h .
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