On the river current a canoe traveled 30 km in 3 hours and 20 min, against the current the canoe traveled 28 km in 4 hours. how far will the canoe go in 1.5 hours on the lake?

12 km

Step-by-step explanation:

Let

x km/h = speed of the canoe on the lake

y km/h = speed of the current

With the current:

Speed = x + y km/h

Distance = 30 km

Time = 3 hours 20 minutes = hours

Thus,

Against the current:

Speed = x - y km/h

Distance = 28 km

Time = 4 hours

Thus,

Add these two equations:

On the lake:

Time = 1.5 hours

Speed = 8 km/h

Distance

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)