Let's break the problem down step by step to find the number of overtime hours worked.
1. Determine the Regular Pay:
The man is paid [tex]$6 per hour for a 40-hour week.
Regular hours worked: \( 40 \) hours.
Regular pay rate: \( \$[/tex]6 \) per hour.
Regular pay: [tex]\( 40 \text{ hours} \times \$6 \text{ per hour} = \$240 \)[/tex].
2. Calculate the Total Payment for Other Times:
The total payment he earned in the week was [tex]\( \$294 \)[/tex].
3. Find the Payment Attributable to Overtime:
Subtract the regular pay from the total payment.
Overtime payment: [tex]\( \$294 - \$240 = \$54 \)[/tex].
4. Determine the Overtime Pay Rate:
The overtime rate is time and a half (1.5 times the regular rate).
Regular rate: [tex]\( \$6 \)[/tex] per hour.
Overtime rate: [tex]\( 1.5 \times \$6 = \$9 \)[/tex] per hour.
5. Calculate the Number of Overtime Hours Worked:
Overtime payment: [tex]\( \$54 \)[/tex].
Overtime rate: [tex]\( \$9 \)[/tex] per hour.
Overtime hours: [tex]\( \frac{\$54}{\$9 \text{ per hour}} = 6 \)[/tex] hours.
So, the number of hours he worked overtime was:
[tex]\[ \boxed{6} \][/tex]
