Aaron and Sam cover the same distance on foot at the speed of 8 km/hr and 6 km/hr. Find the distance covered by each one of them when one takes 15 minutes longer than the other.
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hr. Find the distance covered by each one of them when one takes 15 minutes longer than the other.
Answer:
Step-by-step explanation:
Let's assume that Aaron takes 15 minutes (0.25 hours) longer than Sam to cover the same distance. We'll use the formula Distance = Speed × Time to calculate the distance covered by each of them.
For Aaron:
Speed (A) = 8 km/hr
Time (A) = t (in hours)
For Sam:
Speed (S) = 6 km/hr
Time (S) = t + 0.25 (in hours)
Distance (A) = Speed (A) × Time (A)
Distance (S) = Speed (S) × Time (S)
Now, we want the distances to be the same because they both cover the same distance. So, we can set up an equation:
Distance (A) = Distance (S)
8t = 6(t + 0.25)
Now, solve for t:
8t = 6t + 1.5
Subtract 6t from both sides:
2t = 1.5
Now, divide by 2:
t = 1.5 / 2 = 0.75 hours
Now that we've found the time it takes for Aaron to cover the distance, we can find the distance for both of them.
Distance (A) = Speed (A) × Time (A)
Distance (A) = 8 km/hr × 0.75 hours = 6 km
Distance (S) = Speed (S) × Time (S)
Distance (S) = 6 km/hr × (0.75 + 0.25) hours = 6 km
So, Aaron covers a distance of 6 kilometers, and Sam also covers a distance of 6 kilometers.