Please help me! I don't even know where to start :( my teacher took this question up on friday but i was sick, and we have a test tomorrow!
-Car A travels from Barrie to Subuiry at an average speed of 90km/h
-Car B travels from Subury to Barrie at an average speed of 80km/h
-Barrie and Subury are 300 km apart
(HINT: Recall that Distance=SpeedXTime. THink of the distance that each car is from ONE of the cicties when stetting up youre equations)
a) What does the point of intersection mean in this case?
b) If they left at exactly 9:35 am, at what time will they meet?
Say they travel for t hours
Car A goes 90 * t km
Car B goes 80 * t km
If car A goes distance d, then car B goes 300-d
d =90 t
80 t = 300 - d
80 t = 300 - 90 t
170 t = 300
t = 1.764 hours
1 hour and .764*60 minutes
= 1 hour and 45.882 minutes
call it 1 hour and 46 minutes although we could figure out the seconds
9:45 + 1 hr = 10:45
10:45 + 46 minutes = 11:00 + 31 minutes
so 11:31
No worries, I can help you solve this problem step by step!
a) The point of intersection in this case refers to the moment when both Car A and Car B meet on the road. Since they are traveling towards each other, they will eventually cross paths at some point between Barrie and Subury.
b) To determine the time when Car A and Car B will meet, we need to set up an equation using the distance, speed, and time. Let's start by determining the time it takes for Car A to reach the point of intersection.
Since Car A is traveling at a speed of 90 km/h and the distance between Barrie and the point of intersection is unknown, we can use the formula Distance = Speed x Time. Let's call the time it takes for Car A to reach the point of intersection as t1.
Distance of Car A = Speed of Car A x Time of Car A
Distance of Car A = 90 km/h x t1
Similarly, Car B is traveling at a speed of 80 km/h and the distance between Subury and the point of intersection is also unknown. We can call the time it takes for Car B to reach the point of intersection as t2.
Distance of Car B = Speed of Car B x Time of Car B
Distance of Car B = 80 km/h x t2
Since Car A and Car B meet at the same time at the point of intersection, we can equate the distances traveled by each car to the total distance between Barrie and Subury, which is 300 km.
Distance of Car A + Distance of Car B = Total Distance
90 km/h x t1 + 80 km/h x t2 = 300 km
Now, we have two variables, t1 and t2, and one equation. To solve for these variables, we need another equation. Since they left at exactly 9:35 am, we can represent the time using a 24-hour clock format.
The time it took for Car A to reach the point of intersection (t1) can be represented as 9 hours (from 9 am to 6 pm) plus (35 minutes / 60 minutes) in decimal form. So, t1 = 9.5833 hours.
Similarly, the time it took for Car B to reach the point of intersection (t2) can be represented as t2 = 11.25 hours.
Now, substitute these values into the equation we derived earlier:
90 km/h x 9.5833 hours + 80 km/h x 11.25 hours = 300 km
Finally, solve this equation to find the value of t1 and t2, which will give you the time when Car A and Car B will meet.