For the first part of her journey, Sunita travelled at a speed of 450 m/min and, for the rest of the journey, at a speed 1.4 times of her initial speed. If Sunita travelled a total distance of 33.3 km in 1hour, what was the distance that Sunita travelled at a lower speed?

11.25 km

Speed1 = 450 meter/min

= 450 × \(\frac{3}{50}\) = 27 km/h

speed2 = 1.4 × (speed1)

The total distance traveled in one hour = 33.3 km

Average  speed = \(\frac{Total\; DIstance}{Total \;Time}\)

Speed1 =  27 km/ h

Speed2 =  1.4 × (speed1) = 1.4 × 27 = 37.8 km/h

Total distance traveled in 1 hour = 33.3 km

Let the distance travelled at two speeds be D and (33.3 – D) km

T1 + T2 = 1 hour

\(\frac{D}{S1}\) + \(\frac{33.3 - D }{S2}\) = 1

\(\frac{D}{27}\) + \(\frac{33.3 - D }{27 × 1.4}\) = 1

\(\frac{33.3 - D }{27 × 1.4}\) = 1 - \(\frac{D}{27}\) 

0.4D = 27 × 1.4 - 33.3

D = \(\frac{37.8 - 33.3}{0.4}\)

D = \(\frac{4.5}{0.4}\)

= 11.25 km