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1
The difference between downstream and upstream speed is 2 kmph. If the speed of the boat in still water is three times the speed of the current, find the time taken to cover 18 km downstream.
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Solution: Step 1: Let the speed of the current be x kmph. Step 2: Speed of the boat in still water = 3x kmph. Step 3: Downstream speed = (3x + x) = 4x kmph. Step 4: Upstream speed = (3x - x) = 2x kmph. Step 5: Given, downstream speed - upstream speed = 2 kmph. Step 6: So, 4x - 2x = 2 => 2x = 2 => x = 1 kmph. Step 7: Speed of the boat in still water = 3 * 1 = 3 kmph. Step 8: Downstream speed = 4 * 1 = 4 kmph. Step 9: Time taken to cover 18 km downstream = 18 / 4 = 4.5 hours
2
A person's speed with the current is 15 km/hr and the current's speed is 2.5 km/hr. What is the person's speed against the current?
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Solution: Step 1: Let the person's speed in still water be x km/hr and the speed of the current be y km/hr. Step 2: Given that the person's speed with the current = 15 km/hr and the speed of the current = 2.5 km/hr. Step 3: We know that, speed with current = (speed of person + speed of current). Step 4: So, x + 2.5 = 15. Step 5: Therefore, x = 15 - 2.5 = 12.5 km/hr. Step 6: Now, speed against the current = (speed of person - speed of current) = 12.5 - 2.5 = 10 km/hr.
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