Question

Francis and Marie worked together for $80$ hours. Francis worked thrice as many hours as Marie did. How many hours did they each work?

• A. Francis: $60$ hours
  Marie: $20$ hours
• B. Francis: $40$ hours
  Marie: $20$ hours
• C. Francis: $20$ hours
  Marie: $60$ hours
• D. Francis: $60$ hours
  Marie: $40$ hours

Answer 1

The correct option is A Francis: $60$ hours

Marie: $20$ hours
Let the number of hours Marie worked be $x.$

Given, Francis worked thrice as many hours as Marie did, i.e.,
Number of hours Francis worked
$=3\times$ Number of hours Marie worked
$=3\times x$
$=3x$

According to the question:
Total number of hours Marie and Francis worked together $=80$

$\Rightarrow$ Number of hours Marie worked $+$ Number of hours Francis worked $=80$

$\Rightarrow x+3x=80$

$\Rightarrow 4x=80$

Dividing by $4$ on both the sides

$\Rightarrow \frac{4x}{4}=\frac{80}{4}$

$\Rightarrow x=\frac{20\times 4}{4}$

$\Rightarrow x=20$

$\therefore$ Marie worked for $\underset{–}{20}$ hours and Francis worked for $3\times 20$, i.e, $\underset{–}{60}$ hours.

Hence, option (a.) is the correct answer.