Marks : 1.00 Answer A boat takes 21 hours to travel downstream from point A to point B and...
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Marks : 1.00 Answer A boat takes 21 hours to travel downstream from point A to point B and returns to point C, which is midway between A and B. If the velocity of the’stream is © 3s2km Six kmph and the boat's speed in still water is 18 kmph, what is the distance between A and B? € a ni adit ; iy oo com a 4 E ae z = . rT; a == 3 = —— = aah. os of, === = ea a = === = =— = = = = == ins ! = :. iM - A) 252km - B) 452km. - C) 552km
Show answer & explanation
The total time is the sum of the time taken to travel downstream from A to B and the time taken to travel upstream from B to C (half the distance). Using the relative speeds of the boat and stream, the distance is calculated by solving the linear equation for time.
Step-by-step Derivation:
Step 1: Identify given values. Speed of boat in still water (u) = 18 kmph. Speed of stream (v) = 6 kmph. Total time (T) = 21 hours.
Step 2: Calculate relative speeds. Downstream speed (u + v) = 18 + 6 = 24 kmph. Upstream speed (u - v) = 18 - 6 = 12 kmph.
Step 3: Define distance. Let the distance between A and B be 'D'. The distance from B to C is D/2 (since C is midway).
Step 4: Set up the time equation. Total Time = (Time A to B) + (Time B to C).
21 = (D / 24) + ((D/2) / 12)
Step 5: Simplify the equation.
21 = D/24 + D/24
21 = 2D / 24
21 = D / 12
Step 6: Solve for D.
D = 21 * 12 = 252 km.