Discussion
A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:
Answer: C
Let \( a \) be the hours on foot and \( b \) the hours on the bicycle.
\[ a + b = 9, \qquad 4a + 9b = 61 \]
Substituting \( b = 9 - a \):
\[ 4a + 81 - 9a = 61 \quad\Longrightarrow\quad -5a = -20 \quad\Longrightarrow\quad a = 4 \text{ h} \]
\[ \text{distance on foot} = 4 \times 4 = 16 \text{ km} \]
Setting up the unknowns as times rather than distances is what makes the second equation linear; the question then asks for a distance, so one more multiplication is needed at the end.
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