Video Transcript
A tollbooth collects a five-dollar
toll from every automobile passing by a certain road. The toll collector finds that
during his shift, which lasts 𝑇 hours, the amount of money collected 𝑀, in
dollars, can be estimated by the formula 𝑀 equals five 𝑟𝑇, where 𝑟 is the
average number of cars passing per hour. On Monday, it is estimated that the
rate of cars passing the toll gate is 100 cars per hour. On Tuesday, the rate of cars
passing by the toll gate increases to three cars per minute. What is the percentage increase in
the estimated amount of collected money by the toll collector during his seven-hour
shift?
We are told in the question that
the amount of money can be estimated using the formula 𝑀 is equal to five 𝑟𝑇. The five is the amount of money
paid by every automobile. The 𝑟 is the number of cars per
hour. The 𝑇 is equal to the length of
the shift. In this question, the toll
collector works a seven-hour shift. The only variable that alters
between Monday and Tuesday is the number of cars that passes the tollbooth. On Monday, there are 100 cars that
pass per hour. Whereas on Tuesday, we are told
that three cars pass per minute.
We know that 60 minutes is equal to
one hour. Therefore, we can calculate the
number of cars that pass per hour on Tuesday by multiplying three by 60. This is equal to 180. The number of cars that pass per
hour on Tuesday is 180. To calculate a percentage increase,
we need to divide the actual increase by the original value and then multiply this
by 100, as percentages are out of 100.
The actual increase in cars per
hour is 80, as 180 minus 100 is 80. The original value is 100, as this
was the number of cars that passed on Monday. We need to multiply 80 over 100 by
100. As we’re both dividing and
multiplying by 100, these cancel. This leaves us with a value of 80
percent. As the expected number of cars
increases by 80 percent, the estimated amount of collected money will also increase
by 80 percent.
