Meg rowed her boat

Question

Meg rowed her boat upstream a distance of 12mi and then rowed back to the starting point. The total time of the trip was 8 hours. If the rate of the current was 2 mph, find the average speed of the boat relative to the water.

Answer 1

Time to complete the first leg going upstream is t...

Time to complete the return trip is 8-t

R is the speed of the boat

Speed upstream is R-2

Speed downstream is R+2

Distance = rate * time

Distance/rate = time

total time = time upstream + time downstream

= distance upstream/rate upstream + distance downstream/rate downstream

8 = 12/(r-2) + 12/(r+2)

8(r-2)(r+2) = 12 (r+2) + 12(r-2)

8(r^2-4) = 12r + 24 + 12r - 24

8r^2 - 32 = 24r

8r^2 -24r - 32 =0

r^2 -3r -4 = 0

(r - 4)(r + 1 ) = 0

r=4 or r = -1 <-- disqualified

Upstream: 12/(4-2) = 12/2 = 6 hours

Downstream: 12/(4+2) = 12/6 = 2 hours

Total time is 8 hours, so yes it checks..

The speed of the boat in still water is 4