+171 Emily rows six miles downstream in 1hour and her friend Ashley, rowin 1mile per hour faster, completes the return trip in 2hours.
1 Find the speed of the current (c) and each girl's rowin speed.
2 I Emily and Ashley were rowing separately, who would complete their trip first and by how long? Round to the nearest hundredth, if necessary.
+129852 (1)
Note that Distance / Rate = Time
Let Emily's rate = r mph
Let Ashley's rate = [r + 1] mph
And let the current rate = c
So...Emily travels with the current and we have that
6 / [ r + c ] = 1 hour
6 = [r + c]
c = 6 - r
And Ashley rows against the current .....so
6 / [ r + 1 - c] = 2 hours
6 = 2 [ r + 1 - c]
6 = 2 [ r + 1 - (6 -r) ]
6 = 2 [ 2r - 5]
6 = 4r - 10
16 = 4r
r = 4 mph .....this is Emily's rate
So Ashley's rate = 5 mph
And the rate of the current = 6 - r = 6 - 4 = 2 mph
(2)
For a round trip
Emily would take 6 / [ 4 + 2] + 6 / [ 4 - 2 ] = 1 + 3 = 4 hrs
Ashley would take 6 / [ 5 + 2] + 6 / [5 - 2] = 6/7 + 6/3 = 6/7 + 2 = 20/7 hrs ≈ 2.86 hrs
