Mark reads at an average rate of 30 pages per hour and Mindy reads at an average rate of 40 pages per hour. If Mark starts reading a novel at 4:30 pm and Mindy begins reading the same novel at 5:20pm, at what time will they be reading the same page? Write your answer in 24 hour time.
Answers
Answer:
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Mark reads at an average rate of 30 pages per hour,
while Mindy reads at an average rate of 40 pages per hour.
If Mark starts reading a novel at 4:30 pm,
and Mindy begins reading the same novel at 5:20 pm,
at what time will they be reading the same page?
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Mark DATA:
Rate = 30 page/hr = (1/2) page/minute
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Mindy DATA:
Rate = 40 page/hr = (2/3) page/minute
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Comment: From 4:30 to 5:20 is 50 minutes
In that time Mark has read 50(1/2) = 25 pages.
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EQUATION:
Let the time it takes Mindy to catch up be "x" minutes
Pages read by Mindy = 25 pages + pages read by Mark
(2/3)x = 25 + (1/2)x
4x = 150 + 3x
x = 150 minutes
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150 minutes after 5:20 they will be on the same page.
That would be at 7:50
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Cheers,
Stan H.
Mᴀʀᴋ ʀᴇᴀᴅs ᴀᴛ ᴀɴ ᴀᴠᴇʀᴀɢᴇ ʀᴀᴛᴇ ᴏғ 30 ᴘᴀɢᴇs ᴘᴇʀ ʜᴏᴜʀ,
ᴡʜɪʟᴇ Mɪɴᴅʏ ʀᴇᴀᴅs ᴀᴛ ᴀɴ ᴀᴠᴇʀᴀɢᴇ ʀᴀᴛᴇ ᴏғ 40 ᴘᴀɢᴇs ᴘᴇʀ ʜᴏᴜʀ.
Iғ Mᴀʀᴋ sᴛᴀʀᴛs ʀᴇᴀᴅɪɴɢ ᴀ ɴᴏᴠᴇʟ ᴀᴛ 4:30 ᴘᴍ,
ᴀɴᴅ Mɪɴᴅʏ ʙᴇɢɪɴs ʀᴇᴀᴅɪɴɢ ᴛʜᴇ sᴀᴍᴇ ɴᴏᴠᴇʟ ᴀᴛ 5:20 ᴘᴍ,
ᴀᴛ ᴡʜᴀᴛ ᴛɪᴍᴇ ᴡɪʟʟ ᴛʜᴇʏ ʙᴇ ʀᴇᴀᴅɪɴɢ ᴛʜᴇ sᴀᴍᴇ ᴘᴀɢᴇ?
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Mᴀʀᴋ DATA:
Rᴀᴛᴇ = 30 ᴘᴀɢᴇ/ʜʀ = (1/2) ᴘᴀɢᴇ/ᴍɪɴᴜᴛᴇ
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Mɪɴᴅʏ DATA:
Rᴀᴛᴇ = 40 ᴘᴀɢᴇ/ʜʀ = (2/3) ᴘᴀɢᴇ/ᴍɪɴᴜᴛᴇ
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Cᴏᴍᴍᴇɴᴛ: Fʀᴏᴍ 4:30 ᴛᴏ 5:20 ɪs 50 ᴍɪɴᴜᴛᴇs
Iɴ ᴛʜᴀᴛ ᴛɪᴍᴇ Mᴀʀᴋ ʜᴀs ʀᴇᴀᴅ 50(1/2) = 25 ᴘᴀɢᴇs.
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EQUATION:
Lᴇᴛ ᴛʜᴇ ᴛɪᴍᴇ ɪᴛ ᴛᴀᴋᴇs Mɪɴᴅʏ ᴛᴏ ᴄᴀᴛᴄʜ ᴜᴘ ʙᴇ "x" ᴍɪɴᴜᴛᴇs
Pᴀɢᴇs ʀᴇᴀᴅ ʙʏ Mɪɴᴅʏ = 25 ᴘᴀɢᴇs + ᴘᴀɢᴇs ʀᴇᴀᴅ ʙʏ Mᴀʀᴋ
(2/3)x = 25 + (1/2)x
4x = 150 + 3x
x = 150 ᴍɪɴᴜᴛᴇs
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150 ᴍɪɴᴜᴛᴇs ᴀғᴛᴇʀ 5:20 ᴛʜᴇʏ ᴡɪʟʟ ʙᴇ ᴏɴ ᴛʜᴇ sᴀᴍᴇ ᴘᴀɢᴇ.
Tʜᴀᴛ ᴡᴏᴜʟᴅ ʙᴇ ᴀᴛ 7:50
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