Step-by-step explanation:
there are several things to be considered to solve this.
the strategy is to caucuses the volume of the full "box", and then to deduct the 3-dimensional triangle that is "cut off" from the oil.
then we know the volume of the pool.
next step is to calculate the volume of a "box" with the same layout but is only 20 cm deep.
then we know how much volume can be pumped out in 30 minutes.
and then we divide the whole volume by that small volume to see how many 30-minues units are needed to empty the whole pool.
and then we transform the 30- minutes units into actual minutes or hours.
so, let's begin :
the whole box's volume is
2×1×1.4 = 2.8 m³
the volume of the 3-D triangle we need to subtract is the area of the triangle × width of the pool (this pool width is the height of the 3-D triangle).
2×(1.4 - 0.6) × 1 / 2 = 2×0.8 × 1 / 2 = 1.6/2 = 0.8 m³
so, the volume of the pool is
2.8 - 0.8 = 2 m³
now, how much volume can the pump eliminate in 30 minutes ?
the content of a box
1×2×0.2 = 0.4 m³
as 20 cm = 0.2 m
so, the pump pumps out 0.4 m³ in 30 minutes.
and we need to empty 2 m³.
that means we need
2 / 0.4 = 5
30-minues units = 5×30 = 150 minutes = 2.5 hours.
Colin has to wait 2.5 hours (150 minutes) to empty the complete pool.
denotes the probability of
successes in
independent trials
denotes the probability of success on each of
denotes the probability of failure on the remaining
trials
denotes all possible ways to choose