The speed of the boat in still water is 12 kmph. It can travel downstream through 45 kms in 3 hrs. In what time would it cover the same distance upstream?
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Solution
Let the speed of the current be ‘x’ kmph
∴ Speed downstream = ⇒ 12 + x = 45/3
∴ x = 3 kmph
Required time = hrs.
A man can row one fourth of a kilometer in still water in 1 minutes. The speed (in km/hr) of the man in still water is:
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Solution
Distance covered in one minute = 1/4 km
So distance covered in 60 minutes or 1 hour = 15 km
Required speed = 15 km/hr
There is a road beside a river. Two friends started from a place A, moved to a temple situated at another place B and then returned to A again. One of them moves on a cycle at a speed of 10 km/hr, while the other sails on a boat at a speed of 12 km/hr. If the river flows at the speed of 4 km/hr, which of the two friends will return to place A first?
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Solution
Clearly, the cyclist moves both ways at a speed of 10 km/hr. So, average speed of the cyclist = 10 km/hr.
The boat sailor moves downstream at (12 + 4) i.e., 16 km/hr
and upstream at (12 – 4) i.e., 8 km/hr.
So, average speed of the boat sailor = = 10.666 km/hr.
Since the average speed of the boat sailor is greater, he will return to A first.
A man can row upstream at 8 kmph and downstream at 12 kmph. Find the speed of man at still water and the rate of stream?
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Solution
Speed in still water = (downstream + upstream) = (8 + 12) = 10 kmph.
Rate of stream = (downstream – upstream) = (12 – 8) = 2 kmph
A man can row 7½ kmph in still water. If a river running at 3.5 km an hour, it takes him 1 hour to row to a place and back, how far off is the place? (approximately)
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Solution
Speed downstream = (7.5 + 3.5) kmph = 11 kmph;
Speed upstream = (7.5 – 3.5) kmph = 4 kmph.
Let the required distance be x km. Then,
x/11 + x/4 = 1 ⇔ 11x + 4x = 44 ⇔ 15x = 44 ⇔ x =3 km. (approxmately)
Speed of a boat in standing water is 10 kmph and the speed of the stream is 5 kmph. A man rows to a place at a distance of 120 km and comes back to the starting point. What time will be taken by him to cover the complete journey ?
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Solution
Speed upstream = 10-5 = 5 kmph.
Speed downstream = 10+5 = 15 kmph.
Total time taken = (120/5) + (120/15) hours = 24+8 = 32 hours.
A man rows 750 m in 675 seconds against the stream and returns in minutes. What is his rowing speed in still water ?
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Solution
Rate upstream = m/sec
Rate downstream m/sec = m/sec. = m/sec.
Rate in still water = m/sec. = m/sec
= kmPh = 5 kmph
A man can row upstream 10 kmph and downstream 20 kmph. What is speed of man in still water and speed of stream respectively ?
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Solution
⇒ Speed of man in still water = 1/2 (20 + 10) = 15 kmph
⇒ Speed of stream = 1/2 (20 – 10 ) = 5 kmph
A man can row upstream at 8 kmph and downstream at 13 kmph. What is the speed of the stream ?
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Solution
Speed of stream = (13 – 8) kmph = 2.5 kmph.
A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then what is the velocity of current (in kmph) ?
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Solution
Rate downstream = kmph; Rate upstream = kmph.
∴ Velocity of current = kmph = kmph = kmph,