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Chapter 6: Problem 110

The number of gallons of water used when taking a shower is proportional to the time in the shower. A shower lasting 5 minutes uses 30 gallons of water. How much water is used in a shower lasting 11 minutes?

Short Answer

Expert verified
A shower lasting 11 minutes uses 66 gallons of water

Step by step solution

01

Understand the relation

Firstly, establish the given relationship. The problem states that 5 minutes in the shower uses 30 gallons of water. This is a direct proportion 鈥� the longer the shower (in minutes), the more water (in gallons) is used.
02

Set up the proportion

Set up a proportional equation using the relationship given in the problem. Present it like so: If 5 minutes corresponds to 30 gallons of water, then 11 minutes corresponds to how many gallons? This can be set up in the proportion: \( \frac{5}{30} = \frac{11}{x} \), where x represents the unknown gallons.
03

Solve for 'x'

Cross multiply to solve for 'x'. This results in: \( 5*x = 30*11 \). Divide both sides of this equation by 5 to isolate 'x', yielding: \( x = \frac {30*11}{5} \). Calculate this amount to find the total number of gallons used in an 11-minute shower.

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