Final answer:
To find Kiran's speed from Tortula to Cactus, we set up an equation using the average speed formula, considering the total distance and time of the entire trip. Algebraic manipulation is then used to solve for her speed on the first part of the trip.
Step-by-step explanation:
The question asks us to determine the speed from Tortula to Cactus when given the total distance and time of a two-part journey with different speeds. To solve this problem, we need to use the formula for average speed, which is defined as the total distance traveled divided by the total time taken. From the problem, we know the total distance (287 miles + 392 miles) and total time (15 hours).
Let's denote the speed from Tortula to Cactus as V. Since Kiran increased her speed by 6 mi/h for the second part of the trip, her speed from Cactus to Dry Junction would be V + 6 mi/h.
We can set up our equations by expressing the time taken for each part of the journey as the distance traveled divided by the respective speeds:
- Time from Tortula to Cactus = 287 mi / V
- Time from Cactus to Dry Junction = 392 mi / (V + 6 mi/h)
Since the total time for both parts of the trip is 15 hours, we combine the two expressions to set up our main equation:
287 mi / V + 392 mi / (V + 6 mi/h) = 15 h
We now have a single equation with one variable, V, which we can solve using algebraic manipulation. Once we find the value of V, we will have the average speed Kiran drove from Tortula to Cactus.
If, for instance, a car travels 150 km in 3.2 hours, its average speed would be the distance (150 km) divided by the time (3.2 h), which equals approximately 47 km/h. We can apply this same method of calculation to find Kiran's speed but will need to solve the equation above to find the correct value for her speed from Tortula to Cactus.