Question

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!

Answer 1

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.

Answer 2

i dont get how to do this lol

Answer 3

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)

Answer 4

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