Question

Working alone and at a constant rate, Machine A takes 3 hours to create a widget. Machine B, working alone and at a constant rate, takes x hours to create a widget. Working together, Machine A and B take 12 hours to build two widgets. What is the value of x?

Answer 1

Answer:

Time required by Machine B to create a widget = 4 hours

Step-by-step explanation:

Time taken by Machine A ( $T_{A}$ ) = 3 hours

Time taken by Machine B ( $T_{B}$ )= x hours

Time taken by both machines by working together = 12 hours

The time required to both machines by  working together to finish a task is given by the formula = $\frac{T_{A} {T_{B} } }{T_{A} + T_{B} }$

Put the values in above formula we get

⇒ T =  $\frac{3 x}{3 + x}$

⇒ 12 =  $\frac{3 x}{3 + x}$

⇒ 36 + 12 x = 3 x

⇒ x = - 4 hours

This is the time required by Machine B to create a widget.