Allison drove home at 58 mph, but her brother Austin, who left at the same time, could drive at only 40 mph. When Allison arrived, Austin still had 108 miles to go. How far did Allison drive?
let their times be t hrs
Allison went 58t miles
Austin went 40t miles
58t - 40t = 108
18t = 108
t = 6
Allison went 58(6) or 348 miles
check:
Austin only went 240 miles in those 6 hrs, which is 108 less than Allison
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To find out how far Allison drove, we need to determine the total distance between Allison's and Austin's destinations.
Let's start by calculating the distance Austin traveled at a speed of 40 mph. We know that he still had 108 miles to go when Allison arrived.
Distance traveled by Austin = 108 miles
Now, let's find out how long Allison and Austin have been driving for the same amount of time as they both left at the same time.
To do this, we'll use the formula:
Distance = Speed x Time
Let the time taken by both Allison and Austin be 't' hours.
For Allison:
Distance traveled by Allison = Speed x Time
Distance traveled by Allison = 58t
For Austin:
Distance traveled by Austin = Speed x Time
Distance traveled by Austin = 40t
Since Austin still had 108 miles to go, he would have traveled a lesser distance, which can be expressed as:
Distance traveled by Allison - Distance traveled by Austin = 108 miles
58t - 40t = 108 miles
18t = 108 miles
t = 108 miles / 18
t = 6 hours
Now that we know the time, we can find out how far Allison drove by substituting 't' into the expression for her distance traveled:
Distance traveled by Allison = 58t
Distance traveled by Allison = 58 x 6
Distance traveled by Allison = 348 miles
Therefore, Allison drove 348 miles.
To find the distance that Allison drove, we need to subtract the distance that Austin still had to travel from the total distance between them.
First, we can calculate the distance that Austin still had to go:
Distance = 108 miles
Now, let's calculate the total distance between Allison and Austin. We know that they both drove for the same amount of time, so we can use the formula:
Distance = Speed * Time
Let's assume they both drove for t hours.
For Allison:
Distance (Allison) = 58 mph * t
For Austin:
Distance (Austin) = 40 mph * t
Since they both drove for the same amount of time, we can set these two distances equal to each other:
58t = 40t
Now, we can solve for t:
58t - 40t = 0
18t = 0
t = 0 (Note: This means they both started at the same time, so their travel times are equal)
Now, let's find the total distance between Allison and Austin:
Distance (Total) = 58 mph * t
Distance (Total) = 58 mph * 0 hours
Distance (Total) = 0 miles
Since the total distance between them is 0 miles, we can conclude that Allison and Austin never started from separate locations. Therefore, it is not possible to determine how far Allison drove based on the given information.