Oh, The Grand Old Duke Of York!

Algebra Level 3

Oh, The Grand Old Duke Of York,

He had ten thousand men.

He marched them up

To the top of the hill,

And he marched them down again.

By 2 2 o'clock he was 1 3 \frac {1}{3} of the way up. By 4 4 o'clock he was 3 4 \frac {3}{4} of the way up. Assuming he walked at a constant pace, when did he start?

12:36 11:48 1:24 12:24

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1 solution

Shohag Hossen
May 22, 2015

2 o'clock to 4 o'clock they can go ( 3/4 - 1/3 ) = 5/12

So, In two hours , they can go = 5/12

Now,

5/12 way go in = 2 hours

1 " " " = ( 2*12 ) / 5

So, 1/3 " " " = ( 2 * 12 ) / ( 5 * 3 ) = 1.6

Now ,

1.6 * 60 = 96 minute's .

So, they started in ( 96 minute's ) 1:36 hour's previous from 2 o'clock .

That is why the answer is 12:24 h.

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