Consider the situation for the question below. Toll booths are used to collect money from drivers who use a particular road.

Question

On average, 45 cars pass through a particular toll booth each hour. At 8 am, 75 cars have passed through the toll booth.

Which equation represents the total number of cars, 𝑻, that have passed through the toll booth at 𝒉 (hours after 𝟖 a.m.)?

Answer 1

To represent the total number of cars, \( T \), that have passed through the toll booth at \( h \) (hours after 8 a.m.), we need to consider both the initial number of cars that passed by 8 a.m. and the additional cars that pass through the booth in the following hours.

Initially, at 8 a.m., 75 cars have passed. After 8 a.m., the average number of cars that pass through the toll booth is 45 cars per hour. Therefore, after \( h \) hours, the number of additional cars that would have passed is \( 45h \).

Thus, the total number of cars, \( T \), after \( h \) hours can be expressed using the following equation:

\[ T = 75 + 45h \]

This equation shows that \( T \) is the sum of the 75 cars that were counted by 8 a.m. and the \( 45h \) cars that pass in the \( h \) hours that follow.