| 1. |
In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water. |
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Sol. Let the speed of the motorboat in still water be x kmph. Then,
Speed downstream = (x + 2) kmph; Speed upstream = (x - 2) kmph.
∴ 6/x+2 + 6/x-2 = 33/60
⇔ 11x² - 240x - 44 = 0
⇔ 11x² - 242x + 2x - 44 = 0
⇔ (x - 22) (11x + 2) = 0 ⇔ x = 22.
Hence, speed of motorboat in strill water = 22 kmph.
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| 2. |
A man can row 18 kmph in still water. It takes him trice as long to row up as to row down the river. Find the rate of stream. |
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Sol. Let man’s rate upsream be x kmph. Then, his rate downstream = 3x kmph.
∴ Rate in still water = 1/2(3x + x) kmph = 2x kmph.
So, 2x = 18 or x = 9.
∴ Rate upstream = 9 km/hr, Rate downstream = 27 km/hr.
Hence, rate of stream = 1/2(27 - 9) km/hr = 9 km/hr.
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| 3. |
A man can row upstream at 7 kmph and downstream at 10 kmph. Find man’s rate in still water and the rate of current. |
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Sol. Rate in still water = 1/2 (10 + 7) km/hr = 8.5 km/hr,
Rate of current = 1/2 (10 - 7) km/hr = 1.5 km/hr.
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