Me and my brothers sleep 50 hours each day. My brother T sleeps 6 less hours and c sleeps 14 hours more than T. G and I sleep the same number and we sleep the same number as T and C sleep. How many hours does each person  sleep?
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1 Answer

The third sentence of the question can be interpreted in different ways.


Let T be the number of hours T sleeps. I sleep T+6 hours. C sleeps T+14 hours. G also sleeps T+6 hours (same as me). Together all four of us sleep 50 hours so (T+6)+T+(T+14)+(T+6)=50. From this we get:

4T+26=50, 4T=50-26=24, so T=6 hours. I sleep T+6=6+6=12 hours. G also sleeps 12 hours. C sleeps T+14=20 hours.


The third sentence could mean: together G and I sleep the same number of hours as T and C sleep together. So if G is the number of hours G sleeps then G+T+6=T+T+14, G=T+8.

Then we have (T+6)+T+(T+14)+(T+8)=50, 4T+28=50, 4T=22, T=5½ hours.

I sleep 11½ hours, C sleeps 19½ hours, G sleeps 13½ hours.

I think the second interpretation may be the right one, even though we don’t have whole numbers of hours.

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