Question

A brick layer can build a wall in 6 hours and his apprentice would need 16 hours to build the same wall. When they work together, the apprentice works 5 hours longer than the brick layer. How many hours does each work

Answer 1

Explanation:

The brick layer builds ( 1 wall ) / ( 6 hrs )

That's the same as ( 1/6 wall ) / ( 1 hour )

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The apprentice builds ( 1 wall ) / ( 16 hrs )

That's the same as ( 1/16 wall ) / ( 1 hour )

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Let t = the time that the brick layer works

t + 5 = the timer the apprentice works

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( brick layer's rate ) x ( brick layer's time ) +

( apprentice's rate ) x ( apprentice's time ) = 1

( 1 is the whole job )

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(1/6) · t + (1/16) · (t + 5) = 1

Multiply both sides by 48

8t + 3t + 15 = 48

11t = 33

t = 3

t + 5 = 8

the brick layer works 3 hrs

The apprentice works 8 hrs

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Check:

(1/6) · t + (1/16) · (t + 5) = 1

(1/6) · 3 + (1/16) · (3 + 5) = 1

1/2 + 1/2 = 1

OK