Emily rows six miles downstream in 1 hour and her friend ash

Emily rows six miles downstream in 1 hour and her friend ashley. rowing per hour faster completes the return trip in 2 hours. Find the speed of the current (c) and each girl rowing speed.

Solution

let eb = speed of the Emily\'s boat in still water.

and ab = speed of the Ashley\'s boat in still water.
let c = speed of the current
rate * time = distance = 6 (one way, in this case)
let h = time
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going downstream(Emily), the formula is

(eb + c) * h = (eb + c) * 1 = 6 -----------------------------(1)

We have ab = eb + 1 -------------------------------------------(2)

going upstream(Ashley), the formula is (ab - c) * h = (ab - c) * 2 = 6

implies, ab - c = 3 ----------------------------------------------(3)

substituting (2) in (3),

eb + 1 - c = 3

=====>   eb - c = 2

(1) =====> eb + c = 6

adding both, we get,

2 eb = 8 ========> eb = 4

c = 6 - eb = 2 (from eqn. (1))

ab = eb + 1 = 5

eb = speed of the Emily\'s boat in still water. = 4

ab = speed of the Ashley\'s boat in still water. = 5

c = speed of the current = 2