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# John is using his phone while it is charging. The phone gains 10% every 3 minutes and it drains 7% every 5 minutes. How long will it take his phone to gain a 20% charge?

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Feb 8, 2018

The time required for 20 percent charge gain is $10.33$ minutes

#### Explanation:

percentage gain of charge:
10 in 3 minutes
percentage gain of charge per minute
$= \frac{10}{3}$
If it is charged for $x$ minutes,
percentage gain of charge in $x$ minutes is $= \frac{10}{3} x$
percentage drain of charge:
7 in 5 minutes
percentage gain of charge per minute
$= \frac{7}{5}$
In the same time,
percentage drain of charge in $x$ minutes is $= \frac{7}{5} x$
net gain = gain - drain
$= \frac{10}{3} x - \frac{7}{5} x$
$= \left(\frac{10}{3} - \frac{7}{5}\right) x$
$= \frac{29}{15} x$
For net gain to be 20 percent
$20 = \frac{29}{15} x$
Solving for x
$x = 20 \left(\frac{15}{29}\right)$minutes
The time required for 20 percent charge gain is $\frac{300}{29}$ minutes
$= 10.33$ minutes

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