Erica rows a boat downstream for 60 miles. The return trip upstream took 24 hours longer. If the current flows at 4 mph, how fast does Erica row in still water?

Question

Erica rows a boat downstream for 60 miles. The return trip upstream took 24 hours longer. If the current flows at 4 mph, how fast does Erica row in still water?

She rows=

Evan flies a plane against a headwind for 4599 miles. The return trip with the wind took 10 hours less time. If the wind speed is 5 mph, how fast does Evan fly the plane when there is no wind?

He flighs=

Answer 1

d=rt distance = rate of speed times time traveled

d = (b+c)t = (b-c)(t+24)

b= boat speed in still water, c= current speed, t= time going down stream

(b+4)t = (b-4)(t+24) = 60

t= 60/(b+4)

(b-4)(60/(b+4) + 24) = 60 multiply both sides by b+4

b^2 = 36

b = 6 mph = boat speed in still water

10mph down stream, 2 mph upstream

10(6)= 60 = 2(30)

4599 = d = distance

w=5 mph = wind speed

t against wind = t+10, t= time with the wind

p= speed of the plane with no wind = 68 mph

(p+w)t = 4599

(p+5)t = 4599 = (p-5)(t+10)

t = 4599/(p+5)

(p-5)(499/(p+5) +10) = 4599

multiply both sides by p+5

4599p - 22995 +10p^2 -250 = 4599p + 22995

10p^2 = 46240

p = 68 mph

p^2 = 424

p = sqr424 = about 20.6 mph= planes speed with no wind