Two swimmers at opposite ends of a ninety-foot pool start to swim the length of the pool, one at 3 feet per second and the other
at 2 feet per second. If they swim back and forth for twelve minutes, how many times do they pass each other?
1 answer:
Answer:
20 times
Step-by-step explanation:
The faster swimmer can swim twice the length of the pool in ...
(2·90 ft)/(3 ft/s) = 60 s
The slower swimmer can do it in ...
(2·90 ft)/(2 ft/s) = 90 s
The least common multiple of these times is 180 s = 3 minutes, after which time each swimmer will be back where they started.
A graph of position vs. time shows the swimmers pass 5 times in that 3-minute period. 4 of those are passes when they are going in opposite directions. A 5th pass occurs at one end of the pool, when the faster swimmer passes the slower one going in the same direction.
Since there are 5 passes in each 3-minute period, there are 20 passes in 12 minutes.
The swimmers pass each other 20 times in 12 minutes.
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This question is incomplete because it is not properly and correctly written.
Find attached to this answer a hand drawn sketch diagram of the Aquarium (rectangular prism) showing its dimensions.
Complete Question
The aquarium shown is a rectangular prism that is filled with water. You drop a spherical ball with a diameter of 8 inches into the aquarium. The ball sinks, causing the water to spill from the tank. How much water is left in the tank? Enter your answer to the nearest tenth. (Hint: 1 in³ = 0.00433 gal)
The dimensions of the rectangular prism is given as:
Height = 13 in
Width = 13 in
Length= 20in
The amount of water left is about ____ gallons.
Answer:
The amount of water left in the tank approximately to the nearest tenth is 13.5 gallons (gal) of water
Step-by-step explanation:
Step 1
We are given a rectangular prism with the dimensions :
Height = 13 in
Width = 13 in
Length= 20 in
The first step would be to find the Volume of the Rectangular prism
Volume of the rectangular prism = Length × Width × Height
= 20in × 13in × 13in
= 3380 in³
From the question, we are given the hint that
1 in³ = 0.00433 gal
This means that 1 in³ of an object contains 0.00433 gallons of water.
Therefore, if
1 in³ = 0.00433 gal
3380 in³ =
Cross multiply
2880 in³ × 0.00433 gal
= 14.6354 gal
This means the Aquarium (rectangular prism) contains 14.6354 gallons of water.
Step 2
A spherical ball with the diameter of 8 inches was dropped into the aquarium.
We would find the volume of the spherical ball.
Volume of the Spherical ball = 4/3πr³
Radius = Diameter ÷ 2
= 8 inches ÷ 2 = 4 inches.
Volume of the Spherical ball = 4/3 × π × 4³
Volume of the Spherical ball = 268.08in³
Step 3
We would be converting the Volume of spherical ball to gallons because this gives us the quantity of water spilled due to the sinking of the spherical ball
If , 1 in³ = 0.00433 gal
268.08in³ =
Cross multiply
268.08 in³ × 0.00433 gal
= 1.1607864 gal.
Step 4
The fourth and final step is to subtract the volume of water in the aquarium from the volume of water spilled
14.6354 gal - 1.1607864 gal
= 13.4746136 gal
Approximately to the nearest tenth = 13.5 gal
Therefore, the amount of water left in the tank approximately to the nearest tenth is 13.5 gallons (gal) of water.
