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  • Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she tak

Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus.On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and of the bus.

Answers (1)

Solution:
We know that

Speed = \frac{Distance}{Time}
Time =  Distance / Speed
Let the speed of rickshaw is x and of bus is y.
So, according to question

\frac{2}{x}+\frac{\left ( 14-2 \right )}{y}= \frac{1}{2}Hr

\frac{2}{x}+\frac{12}{y}= \frac{1}{2}\cdots (1)

 \frac{4}{x}+\frac{10}{y}= \frac{39}{60}\, Hour\cdots (2)

Solve eq. (1) and (2)

\left ( \frac{2}{x}+\frac{12}{y} = \frac{1}{2}\right )\times 2

\frac{4}{x}+\frac{24}{y}= 1

\frac{4}{x}+\frac{10}{y}= \frac{39}{60}
–     –      –

\frac{24}{y}-\frac{10}{y}=1- \frac{39}{60}

\frac{24-10}{y}= \frac{60-39}{60}

\frac{14}{y}= \frac{21}{60}
21y = 840

y= \frac{840}{21}= 40
Put y = 40 in eq. (1)

\frac{2}{x}+\frac{12}{40}= \frac{1}{2}

\frac{2}{x}= \frac{20-12}{40}

\frac{2}{x}= \frac{8}{40}
40 = 4x
x = 10
Speed of rickshaw = 10 km/h
Speed of bus = 40 km/h

Posted by

infoexpert27

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