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

Answer:

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

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