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.

BOSEOK
Aug 29, 2017

#1**+2 **

(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

CPhill
Aug 29, 2017