Answer:
66 mph
Step-by-step explanation:
In this explanation, I will assume that you are measuring in miles per hour (mph).
Because the trip took [tex]7 \frac{2}{3}=\frac{23}{3}[/tex] hours, then we can divide 506 miles by [tex]\frac{23}{3}[/tex] to find that [tex]\frac{506}{\frac{23}{3}}=66[/tex] mph.
Taking into account the definition of speed, you get that the speed of the bus is 66 [tex]\frac{miles}{hours}[/tex].
Speed is a physical quantity that expresses the relationship between the space traveled by an object and the time used for it. In other words, velocity can be defined as the amount of space traveled per unit of time with which a body moves and can be calculated using the expression:
[tex]Speed=\frac{distance traveled}{time}[/tex]
In this case:
First, it is convenient to convert the mixed fraction corresponding to the time to improper. To do this, the integer is multiplied by the denominator, to which the numerator is added. Divide this result by the denominator. The denominator of the improper fraction will be the same as the mixed number had. In summary:
[tex]a\frac{b}{c} =\frac{axc+b}{c}[/tex]
In this case:
[tex]7\frac{2}{3} =\frac{7x3+2}{3}[/tex]
Solving:
[tex]7\frac{2}{3} =\frac{21+2}{3}[/tex]
[tex]7\frac{2}{3} =\frac{23}{3}[/tex]
Then, the trip took [tex]\frac{23}{3}[/tex] hours. So, replacing the known data in the speed definition:
[tex]Speed=\frac{506 miles}{\frac{23}{3} hours}[/tex]
Solving:
Speed= 66 [tex]\frac{miles}{hours}[/tex]
Finally, the speed of the bus is 66 [tex]\frac{miles}{hours}[/tex].
