The average speed is the ratio of the total distance traveled to the time taken
The correct option for the interval with the greatest average speed is option (1) the first hour to the second hour
The procedure by which the above option was arrived at is as follows:
The given table of values for the graph is presented as follows;
[tex]\begin{array}{|c|cc|} \mathbf{Time}&&\mathbf{Distance}\\1&&40\\2&&110\\4&&180\\6&&230\\8&&350\\10&&390\end{array}\right][/tex]
[tex]Average \ speed = \dfrac{Distance}{Time}[/tex]
The average speed of each interval in distance per hour are given as follows;
[tex]First \ and \ second \ hour, \ average \ speed = \dfrac{110 - 40}{2 - 1} = 70[/tex]
[tex]Second \ and \ fourth \ hour, \ average \ speed = \dfrac{180 - 110}{4 - 2} = 35[/tex]
[tex]Sixth \ and \ eight \ hour, \ average \ speed = \dfrac{350 - 230}{8 - 6} = 60[/tex]
[tex]Eight \ and \ tenth \ hour, \ average \ speed = \dfrac{390 - 350}{10 - 8} = 20[/tex]
Therefore the interval in which their average speed was the greatest is the first hour to the second hour
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