Question

Alejandro wrote an equation to fit the following scenario.

A person driving a pick-up truck and another person driving a motorcycle arrange to meet at a park. The pick-up truck driver took twice as long to arrive while driving at an average speed of 45 mph. The motorcyclist drove 55 mph and had a 23 miles less to drive.

Alejandro’s work:
t = number of hours for the pick-up truck driver to complete the trip
Equation: 55 (2 t) minus 23 = 45 (t)

Which statements identify Alejandro’s errors? Select the two correct answers.
He should have added the 23 to the motorcyclist’s distance instead of subtracting to balance the equation.
He should have written 45(2t) for the pick-up truck driver’s distance, since the he took twice as long.
He should have written 55(t) for the motorcyclist’s distance since t = number of hours for the pick-up truck driver to complete the trip.
He should have written 55 (one-half t) for the motorcyclist’s distance since it only took half the time as the pick-up truck driver.
He should have translated the scenario as motorcycle distance + pick-up truck distance = 23 since 23 is the distance mentioned.

Answer 1

Distance, rate and time problems are a standard application of linear equations. When solving these problems, use the relationship rate (speed or velocity) times time equals distance.

\[r\cdot t=d\]

For example, suppose a person were to travel 30 km/h for 4 h. To find the total distance, multiply rate times time or (30km/h)(4h) = 120 km.

The problems to be solved here will have a few more steps than described above. So to keep the information in the problem organized, use a table. An example of the basic structure of the table is below: