Yes, Elias got his food before reaching the potluck.
Step-by-step explanation:
Elias left home at 7:00 one morning, determined to make the ten-mile trip to Leaders on a bicycle. Soon thereafter, Elias' parent noticed he had forgotten his potluck dish on the kitchen table, got into the family car, and tried to catch up with the forgetful child. Elias had a fifteen-minute head start, and was pedaling at 12 mph, while the parent pursued at 30 mph. Was Elias reunited with his potluck food before reaching Leaders that day? If so, where? If not, at what time was the food delivered?
Let's set x as the time after the parent leaves as x (time after the first 15-minute headstart)
When the two meet, it means that the distance is equal. Remember, distance = time * speed.
Using this, we know that Elias had a 15-minute headstart at 12 mph, which means that he had 0.25 of an hour. Thus, Elias had a 0.25 * 12 mile headstart.
We can write this equation for the distance Elias traveled.
0.25 * 12 + 12 * x
And this equation for the distance his parent traveled.
30 * x
These equations need to be equal so that the two meet.
0.25 * 12 + 12 * x = 30 * x
Simplify.
3 + 12x = 30x
Subtract 12x from both sides.
3 = 18x
Divide both sides by 18.
x = 1/6
So, it took 1/6 of an hour, which is 10 minutes, for the parent and Elias to meet.
If Elias were to get the food before he reached the potluck, the distance he traveled (0.25 * 12 + 12 * x) needs to be less than 12.
Plug 1/6 in for x.
0.25 * 12 + 12 * 1/6 =
3 + 2 = 5
Elias traveled 5 miles before his parent met him.
So, Elias did get his food before reaching Leaders.
Just in case, let's double-check this answer.
Using the distance = speed * time formula, we know that time = distance/speed. Elias's parent had to travel 5 miles at 30 mph, so it would have taken 1/6 of an hour to drive 5 miles.
Elias traveled at 12 mph for 1/6 + 1/4 of an hour, so he traveled:
(1/6 + 1/4) * 12 =
(4/24 + 6/24) * 12 =
10/24 * 12 =
120/24 = 5 miles
Thus, the previous answer is right.
I hope this helps! Feel free to ask any questions!
