question_answer

An aeroplane flies around a square field ABCD of each side 1000 km. Its speed along AB is \[250\text{ }km{{h}^{-1}},\]along BC\[500\text{ }km{{h}^{-1}},\] along CD \[200km{{h}^{-1}},\]and along DA \[100\text{ }km{{h}^{-1}}\]. Its average speed (in\[km{{h}^{-1}}\])over the entire trip is

A)  225.5                   

B)         175.5

C)  125.5                   

D)         310.5

E)  190.5

Correct Answer: E

Solution :

Time along the \[AB=\frac{1000}{250}=4\text{ }h\] Time along the \[BC=\frac{1000}{500}=2\text{ }h\] Time along the\[CD=\frac{1000}{200}=5\text{ }h\] Time along the \[AD=\frac{1000}{100}=10\text{ }h\] Average speed \[=\frac{Total\,dis\tan ce}{Total\,time}\]                                 \[=\frac{4\times 1000}{4+2+5+10}=\frac{4000}{21}\] \[=190.5\text{ }km/h\]