Iwillget770 wrote:
Lee is planning a trip and estimates that, rounded to the nearest 5 kilometers (km), the length of the trip will be 560 km and that, rounded to the nearest
hour, the driving time for the trip will be 7 hours. If these estimates are correct, then Lee’s average driving speed during the trip will be between __
x__ kilometers per hour and _
y__ kilometers per hour, where
x <
y.
From the values given in the table, select for
x and for
y the values that complete the statement in such a way that the interval between the selected values includes all possible average speeds for Lee's trip and
y –
x is minimal. Make only two selections, one in each column.
Say distance is between 5 to 10: Nearest 5 km means the distance is rounded off to 5, if the distance is <7.5, otherwise rounded off to 10.
Thus, in case of 560, the distance would lie in range => \(557.5 \leq D < 562.5\)
Similarly, the hours would be in range => \((6-\frac{1}{2}*\frac{1}{4}) \leq D < (6+\frac{1}{2}*\frac{1}{4})\) = \(6.875 \leq D < 7.125\)
Minimum average speed = smallest distance in maximum time = \(\frac{557.5}{7.125}=78.25\)
Maximum average speed = largest distance in minimum time = \(\frac{562.5}{6.875}=81.81\)
Thus, the range should contain all values from 78.25 to 81.81
Since y-x has to be minimal, look for an option just below 78.25 for x, and look for an option just above 81.81 for y.
x = 76 and y=82