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# algebra 2

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At 6 o'clock, the tip of the hour hand was 23cm from the tip of the minute hand. At 9 o'clock, this distance was only 17cm. By how many centimeters does the minute hand's length exceed the hour hand's length?  ( no diagram provided) I tried to use Pythagorean and in the end, I didn't know what to do after I went from there.

Apr 30, 2019

#1
+1

At 6 o'clock, the tip of the hour hand was 23cm from the tip of the minute hand. At 9 o'clock, this distance was only 17cm. By how many centimeters does the minute hand's length exceed the hour hand's length?  ( no diagram provided) I tried to use Pythagorean and in the end, I didn't know what to do after I went from there.

You were on the right track with Pythagorean.  At six o'clock, the hands are in a straight line so we know the total length of the two hands is 23 cm.  One hand length we will call L so the other hand is (23 – L).

Draw your triangle when the hour hand is at nine and the minute hand at twelve.  One hand length is L, the other hand length is (23 – L), and the hypotenuse is 17.

so, by the Pythagorean Theorem,                    L2 + (23 – L)2 = 172

multiply it on out                                               L2 + (529 – 46L + L2) = 289

remove parentheses and rearrange terms      2L2 – 46L + 240 = 0               (240 came from 529 minus 289)

this will factor to                                               (2L – 16)(L – 15) = 0

set each term to zero                                       2L – 16 = 0     thus  L = 8

L – 15 = 0     thus  L = 15

the minute hand is longer, so it's the one that's 15 and the hour hand is 8

so the minute hand length exceeds the hour hand length by 15 – 8 = 7 cm

17 cm

May 1, 2019

#1
+1

At 6 o'clock, the tip of the hour hand was 23cm from the tip of the minute hand. At 9 o'clock, this distance was only 17cm. By how many centimeters does the minute hand's length exceed the hour hand's length?  ( no diagram provided) I tried to use Pythagorean and in the end, I didn't know what to do after I went from there.

You were on the right track with Pythagorean.  At six o'clock, the hands are in a straight line so we know the total length of the two hands is 23 cm.  One hand length we will call L so the other hand is (23 – L).

Draw your triangle when the hour hand is at nine and the minute hand at twelve.  One hand length is L, the other hand length is (23 – L), and the hypotenuse is 17.

so, by the Pythagorean Theorem,                    L2 + (23 – L)2 = 172

multiply it on out                                               L2 + (529 – 46L + L2) = 289

remove parentheses and rearrange terms      2L2 – 46L + 240 = 0               (240 came from 529 minus 289)

this will factor to                                               (2L – 16)(L – 15) = 0

set each term to zero                                       2L – 16 = 0     thus  L = 8

L – 15 = 0     thus  L = 15

the minute hand is longer, so it's the one that's 15 and the hour hand is 8

so the minute hand length exceeds the hour hand length by 15 – 8 = 7 cm

17 cm

Guest May 1, 2019