Two cars drive from town A to town B at constant speeds. The blue car travels 25 miles per hour and the red car travels 60 miles per hour. The blue car leaves at 9:30 am and the red car leaves at noon. The distance between the two towns is 150 miles. Who will get there first? Write the system of linear equations that represents this situation.
A detailed explanation would be helpful. Thank you!
time = distance/rate
blue car's time = 150/25 = 6 hrs
red car's time = 150/60 = 2.5 hrs
so, since the blue car left at 9:30 am, it will arrive 6 hours later , at 3:30 pm
the red car left at noon, so will arrive 2.5 hours later, at 2:30 pm
Why would you need to introduce variables, and form a system of equations ????
The question is an example of overkill and making a problem more difficult than it has to be.
a) y=25x+62.5
y=60x
The red car will make it first. It will take the red car about 2 and a half hours to make it, while it will take the blue car 6 hours to make it.
b) The graphs intersect at about (1.8, 110)
i dont get how to do this lol
Let x is speed of car, y is arrival time from A to B, t is depature time
Linear equation. Y= 150/x +t
Blue car. 150/25 +9h30 = 15h30
Red car. 150/60 + 12h=14h30
To determine who will get to town B first, we need to compare the time it takes for each car to travel from town A to town B.
First, let's determine the time it takes for the blue car to travel from town A to town B. We can use the formula: Time = Distance / Speed.
Since the distance between the two towns is 150 miles and the blue car travels at a speed of 25 miles per hour, we can plug in these values into the formula:
Time for blue car = 150 miles / 25 miles per hour
Time for blue car = 6 hours
Now, let's determine the time it takes for the red car to travel from town A to town B. Using the same formula:
Time for red car = 150 miles / 60 miles per hour
Time for red car = 2.5 hours
However, we need to consider that the blue car left at 9:30 am and the red car left at noon. We need to account for the time difference.
From 9:30 am to noon, there is a time difference of 2.5 hours (12:00 pm - 9:30 am), which is the same as the time it takes for the red car to travel from town A to town B. Therefore, we can conclude that when the red car arrives in town B, the blue car will have been traveling for 2.5 hours.
So, let's calculate the time it takes for the blue car to travel from 9:30 am to when the red car arrives:
Time for blue car = 2.5 hours + 6 hours
Time for blue car = 8.5 hours
Now, we can compare the times for both cars. The red car takes 2.5 hours to travel from town A to town B, while the blue car takes 8.5 hours. Since the red car arrives first, we can conclude that the red car will get to town B first.
To write the system of linear equations representing this situation, we can use the equation "Distance = Speed * Time."
For the blue car:
Distance = 25t (where t is the travel time in hours)
For the red car:
Distance = 60(t - 2.5) (since the red car started 2.5 hours later)
Both equations represent the distance traveled by each car as a function of time.