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3 years ago

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A vehicle 1 1/8 uses gallons of gasoline to travel 13 1/2 miles. At this rate, how many miles can the vehicle travel per gallon

of gasoline?

2 answers:

alexgriva [62]3 years ago

3 0

Answer: 12 miles per gallon

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Ivan3 years ago

3 0

Answer:

<em>The vehicle can travel 12 miles per gallon of gasoline</em>

Step-by-step explanation:

<u>Proportions</u>

A vehicle uses 1 1/8 gallons of gasoline to travel 13 1/2 miles.

It's required to find the rate of miles per gallon of gasoline consumption of the vehicle.

First, we convert all the mixed fractions to improper fractions:

$1\frac{1}{8}=1+\frac{1}{8}=\frac{9}{8}$

$13\frac{1}{2}=13+\frac{1}{2}=\frac{27}{2}$

The rate of consumption is:

$\displaystyle \frac{\frac{27}{2}}{\frac{9}{8}}$

Operating:

$\displaystyle \frac{\frac{27}{2}}{\frac{9}{8}}=\frac{27}{2}\cdot\frac{8}{9}=12$

The vehicle can travel 12 miles per gallon of gasoline

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Step-by-step explanation:

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$k= 2 \to s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\$

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Calculate the sum $(S=s_1+s_2+s_3+......+s_n)$

$S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\$

When $s_n \ \ dt_{n \to 0}$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\$

$\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}$

In point 2: $\sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}$

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$k= 1 \to s_1 = \frac{1}{(1+6)(1+7)}\\\\$

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