and 11¼ minutes as 675 seconds.
Rate upstream = | ❨ | 750 | ❩m/sec | = | 10 | m/sec. |
675 | 9 |
Rate downstream = | ❨ | 750 | ❩m/sec | = | 5 | m/sec. |
450 | 3 |
∴ Rate in still water = | 1 | ❨ | 10 | + | 5 | ❩m/sec |
2 | 9 | 3 |
= | 25 | m/sec |
18 |
= | ❨ | 25 | x | 18 | ❩km/hr |
18 | 5 |
= 5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.
Speed upstream = (5 - 1) kmph = 4 kmph.
Let the required distance be x km.
Then, | x | + | x | = 1 |
6 | 4 |
⟹ 2x + 3x = 12
⟹ 5x = 12
⟹ x = 2.4 km.
Rate downstream = | ❨ | 16 | ❩kmph = 8 kmph. |
2 |
Rate upstream = | ❨ | 16 | ❩kmph = 4 kmph. |
4 |
∴ Speed in still water = | 1 | (8 + 4) kmph = 6 kmph. |
2 |
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
∴ | 30 | + | 30 | = 4 | 1 |
(15 + x) | (15 - x) | 2 |
⟹ | 900 | = | 9 |
225 - x^{2} | 2 |
⟹ 9x^{2} = 225
⟹ x^{2} = 25
⟹ x = 5 km/hr.
Speed downstream = (10 + x) mph,
Speed upstream = (10 - x) mph.
∴ | 36 | - | 36 | = | 90 |
(10 - x) | (10 + x) | 60 |
⟹ 72x x 60 = 90 (100 - x^{2})
⟹ x^{2} + 48x - 100 = 0
⟹ (x+ 50)(x - 2) = 0
⟹ x = 2 mph.
Speed downstream = (x + 3) kmph,
Speed upstream = (x - 3) kmph.
∴ (x + 3) x 1 = (x - 3) x | 3 |
2 |
⟹ 2x + 6 = 3x - 9
⟹ x = 15 kmph.
Distance travelled = | ❨ | 18 x | 12 | ❩km = 3.6 km. |
60 |
Rate downstream = | ❨ | 1 | x 60 | ❩km/hr = 6 km/hr. |
10 |
Rate upstream = 2 km/hr.
Speed in still water = | 1 | (6 + 2) km/hr = 4 km/hr. |
2 |
∴ Required time = | ❨ | 5 | ❩hrs = 1 | 1 | hrs = 1 hr 15 min. |
4 | 4 |
Speed downstream = | ❨ | 4 | ❩ | km/hr. |
x |
Speed upstream = | ❨ | 3 | ❩ | km/hr. |
x |
∴ | 48 | + | 48 | = 14 or x = | 1 | . |
(4/x) | (3/x) | 2 |
So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.
Rate of the stream = | 1 | (8 - 6) km/hr = 1 km/hr. |
2 |
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