A car is traveling south at a speed of 68 mi/h from Dallas toward San Antonio. Dallas is about 272 miles north of San Antonio. A truck is traveling north from San Antonio to Dallas at a speed of 71 mi/h. When and where will they pass each other?
1. Create a table to record the highway distance from San Antonio for 0-5 hours in one-hour intervals.
2. Graph the information in your table. Put time on the x-axis.3. What do the y-intercepts on your graph mean?
4. Where do the cars pass each other?
5. Which vehicle reaches its’ destination first?
To answer these questions, we can follow these steps:
1. Create a table to record the highway distance from San Antonio for 0-5 hours in one-hour intervals:
| Time (hours) | Car Distance from San Antonio (miles) | Truck Distance from San Antonio (miles) |
|--------------|--------------------------------------|---------------------------------------|
| 0 | 272 | 0 |
| 1 | 204 | 71 |
| 2 | 136 | 142 |
| 3 | 68 | 213 |
| 4 | 0 | 284 |
| 5 | -68 | 355 |
2. Graph the information in your table. Put time on the x-axis and distance on the y-axis.
Let's plot the points on a graph:
3. The y-intercepts on the graph represent the initial distances between each vehicle and San Antonio. For the car, the y-intercept is 272 miles, which means the car started 272 miles north of San Antonio. For the truck, the y-intercept is 0 miles, indicating that the truck started from San Antonio itself.
4. The vehicles pass each other when their distances from San Antonio are equal. From the table, we can see that at 4 hours, the car's distance is 0 miles and the truck's distance is 284 miles. Therefore, they pass each other after 4 hours, somewhere on the highway.
5. To determine which vehicle reaches its destination first, we need to compare how long it takes for each vehicle to reach its destination. The car has a distance of 272 miles to cover, while the truck has a distance of 0 miles. Since both vehicles are traveling at different speeds, we need to calculate their travel times:
Time taken by the car = Distance/Speed = 272 miles / 68 mi/h = 4 hours
Time taken by the truck = Distance/Speed = 272 miles / 71 mi/h ≈ 3.83 hours
Therefore, the truck reaches its destination (Dallas) first, as it takes approximately 3.83 hours, while the car takes 4 hours to reach its destination (San Antonio).
So, the truck arrives in Dallas first, and the car arrives in San Antonio last.
I will assume you meant to state that they left at the same time.
Let the distance covered by the southbound be x
let the distance covered by the northbound be 272-x
time for southbound = x/68
time for northbound = (272-x)/71
solve: x/68 = (272-x)/71
71x = 18496 - 68x
139x = 18496
x = 133.06
the southbound car went 133.06 , and the northbound went 138.94 miles when they met
time = 133.06/68 = 1.957 hrs
( check: 138.94/71 = 1.957 hrs )
Just follow the instructions for the remaining part of the question.