A woman went on a journey by walking,by bus and by matatu. She went by bus for $\frac{4}{5}$ of the distance, then by matatu $\frac{2}{3}$ of the rest of the distance, then walked the remaining distance

A woman went on a journey by walking,by bus and by matatu. She went by bus for $\frac{4}{5}$ of the distance, then by matatu $\frac{2}{3}$ of the rest of the distance, then walked the remaining distance. The distance travelled by the bus was 55 km more than the distance walked. Find the total distance

Answers

Let the distance be x km

therefore by bus = $\frac{4}{5}x$ km

By matatus = $\frac{2}{3}$ x $\frac{1}{5}x$ = $\frac{2}{15}x$

Walked = x - ($\frac{4}{5}x$ + $\frac{2}{15}x$)

= x - $\frac{14}{15}x$ = $\frac{1}{15}x$

$\frac{4}{5}x$ - $\frac{1}{15}x$ = 55

$\frac{12x - x}{15}$ = 55; $\frac{11}{15}x$ = 55

therefore x = $\frac{55\times 15}{11}$ = 75 km

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johnmulu answered the question on March 2, 2017 at 13:41

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