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Question

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 the bus in km/hr respectively.

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Solution

Let the speed of the rickshaw be x km/min and the speed of the bus be y km/min.
Since time = distance/speed,
2x+12y=30;
4x+10y=39.
Substituting 1x as u and 1y as v, we get (Where x0,y0)
2u+12v=30(1)
4u+10v=39(2)

Multiplying equation (1) by 2, we get 4u+24v=60(3)
Subtracting equation (2) from equation (3), we get 14v = 21 v=32

Putting v=32 in equation (1), we get,
2u+12×32=302u=3018
u=122=6.

Therefore, x=16 km/min and y=23 km/min.

To get the speed in km/hr, we multiply each speed with 60, since 1 hr = 60 min.
Therefore,
x=16×60=10 km/hr
y=23×60=40 km/hr

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