Question

john is filling a bathtub that is 18 inches deep. he notices that it takes two minutes to fill the tub with three inches of water. he estimates that it will take ten more minutes for the water to reach the top of the tub if he continues at the same rate. is he correct?

Answer 1

John is correct in thinking that it will take 10 minutes to fill the tub with the needed amount of water at the rate it's going.

Further Explanation:

To solve this problem,

1. Sort out the given.

2. Identify the unknown.

3. Set up the equation that will be used to solve the problem.

4. Substitute the values into the given equation.

5. Solve for the unknown.

STEP 1: Identify the given:

depth of bathtub = 18 inches

rate of filling = 3 in/2 min

STEP 2: Identify the unknown:

time to fill bathtub with water = ?

STEP 3 & 4:

The rate of filling, as stated in the problem, is 3 inches for every 2 minutes. Using this equality, the time needed to fill an 18 inch deep bath tub can be solved using the equation below:

$time \ to \ fill \ bathtub = 18 \ in \ (\frac{2 \ min}{3 \ in})\\ \\time \ to \ fill \ bathtub \ = 12 \ min$

It will take 12 minutes to fill the bathtub.

STEP 5:

During the first 2 minutes, John observed that 3 in of water had already been put in.

He, therefore, needs to wait for 10 more minutes for the rest of the bath tub to be filled with water.

Learn More

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Keywords: rate, ratio and proportion

Answer 2

Depth of the bathtub = 18 inches
Time taken to fill 3 inches of the bathtub = 2 minutes
Then
The amount of depth needed to fill with water = (18-3) inches
                                                                         = 15 inches
Time required to fill 15 inches of the bathtub = (15*2)/3 minutes
                                                                       = 30/3 minutes
                                                                       = 10 minutes
So John is correct in thinking that it will take 10 more minutes for the water to reach the top of the tub if he continues at the same rate.