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turn over both the hourglasses at once....

when the 4 min. hourglass runs out, turn it over...

when the 7 min. hourglass runs out, turn it over...

when the 4min. hourglass runs out, turn over the 7 min. hourglass.

now 8 minutes are over... and only one min. is left in 7 min. hourglass...

after the 7 min. hourglass runs out.. 9 minutes are complete

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Start both hourglasses

When the 4min runs out, turn it over - 4mins elapsed

When the 7min runs out, turn both over - 7mins elapsed (4mins has 1min)

When the 1min in the 4min runs out, turn over the 7min - 8mins elapsed (7min has 1min)

Let the 1min in the 7min run out - 9mins elapsed

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