Two boats are moving towards each other from harbours that are 144 km apart. One boat is moving at 63 km. h-1 and the other boat at 81 km. h-1 . If both started their journey at the same time, how long will they take to pass each other?

1 hour

Step-by-step explanation:

Let distance1 = x km

Distance2 = 144 - x

Speed S1 = 63 kph

Speed S2 = 81 kph

Time = Distance / Speed

When the jets pass each other

(144-x) / 81 = x/63

63(144-x) = 81x

9072 - 63x = 81x

x = 9072 / 144

x = 63 km

Time = 63/63 = 1 hour

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

answer: finding the extract measurements and knowing the points

step-by-step explanation: