Question

3 Elena and Jada are 32 miles apart on a path when they start

moving toward each other, Elena runs at a constant speed of 6
miles per hour, and lada walks at a constant speed of 2 miles per
hour, How long does it take until Elena and Jada meet? Complete
the table to show your reasoning,
(table: 8 points total-
2 points
for each section)
Elapsed Time
Distance Apart
(hours)
(miles)
0
32
1
24
2
8 을
Hours it takes Elena and Jada to meet: (2 points)

Answer 1

The hours it takes Elena to meet Jada = 4 hours

Explanation:

The distance between Elena and Jada = 32 miles

The speed with which Elena runs = 6 miles per hour

The speed with which Jada walks = 2 miles per hour

Let t, represent the time it takes until Elena and Jada meets, we have;

Distance = Speed × Time

The total distance covered by both Elena and Jada before they meet = The distance between them = 32 miles

The distance covered by Elena before meeting Jada = Elena's speed × The time that elapsed for them to meet

∴ The distance covered by Elena before meeting Jada = 6 mph × t

The distance covered by Jada before meeting Elena = Jada's speed × The time that elapsed for them to meet

∴ The distance covered by Jada before meeting Elena = 2 mph × t

The total distance covered by both Elena and Jada before they meet = The distance covered by Elena before meeting Jada + The distance covered by Jada before meeting Elena = 32 miles

∴ The total distance covered by both Elena and Jada before they meet = 6 mph × t + 2 mph × t = 32 miles

t × (6 mph + 2 mph) = 32 miles

t × 8 mph = t × 8 miles/hour = 32 miles

t = 32 miles/(8 miles/hour) = 4 hours

The time it takes until Elena and Jada meets = t = 4 hours