solve the following problem
1. One pipe can fill a fire truck water tank in 10 minutes and another can fill it in 20 minutes. If both pipes will be open at same time, how long will it take them to finish filling the water tank?
2. Edna can clean the room in 3 hours while cherry can clean the same room in 4 hours. If they work together how long will it take them to clean the room?
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Answer:
1.) 6.67 minutes
2.) 1.71 hours
Step-by-step explanation: The questions involve work problems. In this case, if two things work together to finish a certain task, the total time will be reduced. The following are detailed solutions:
1.) Step 1: We need to get first the rate of work done by each pipe to fill the firetruck water tank alone. Let us label the pipes: Pipe A and Pipe B.
Pipe A can fill x/10 of the tank in 1 minute while Pipe B can fill x/20 with the same tank.
Step 2: Let us construct our equation.
x/10 + x/20 = 1
Step 3: Using algebraic manipulation, we need to find the value of x by multiplying both sides of the equation by the LCD of 10 and 20 which is 20.
20(x/10 + x/20 = 1)
2x + x = 20 (Combine like terms)
3x = 20 (Divide both sides by 3)
x = 20/3
x = 6 ⅔ or 6.67 minutes
Therefore, both pipes can fill the water tank together in 6.67 minutes.
2.) Step 1: Just like what we did in #1, we let the work done by Edna as x/3 while Cherry as x/4.
x/3 + x/4 = 1
Step 2: Do the algebraic manipulation by multiplying both sides by 12 which is the LCD of 3 and 4.
12(x/3 + x/4 = 1)
4x + 3x = 12 (Combine like terms)
7x = 12 (Divide both sides by 7)
x = 12/7
x = 1.71 hours
Therefore, Edna and Cherry can clean the room together in 1.71 hours.
Check more word problems here: brainly.ph/question/25546
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