Eddie and his sister walked from home to school. His sister started walking at 8:00am at an average speed of 50 m/min. Eddie started walking at 8:05 at a speed of 60 m/min. Eddie caught up with his sister at mid-point between the school and his home. Find the distance between Eddie's home and the school.
Please help, thank you so much
Let the distance between home and school be 2x
So they met after x metres.
Sister went for t minutes at 50 m/min , so x = 50t
Eddie went for (t-5) minutes at 60 m/min so x = 60(t-5)
but those are equal, so
60(t-5) = 50t
60t - 300 = 50t
t = 30
then x = 50(30) m = 1500 m
and the school is 3000 m or 3 km from home
Got it. Thanks
To solve this problem, we need to find the distance between Eddie's home and the school. Let's break it down step by step:
Step 1: Find the time it took for Eddie to catch up with his sister.
Since Eddie started walking 5 minutes after his sister, we can assume that they met after the same amount of time. Let's call this time "t" in minutes.
Step 2: Identify the distances traveled by Eddie and his sister.
Eddie's sister started walking at 8:00 am, which means she walked for t minutes before they met. Since her average speed is 50 m/min, the distance she traveled is 50t meters.
Eddie started walking at 8:05 am, which means he walked for t - 5 minutes before they met. Since his speed is 60 m/min, the distance he traveled is 60(t - 5) meters.
Step 3: Determine the mid-point between the school and Eddie's home.
Let's call the distance between Eddie's home and the school "d" meters. Since they met at the mid-point, the distance traveled by each person is half of the total distance, which is d/2.
Step 4: Set up an equation based on the distances traveled.
The equation is: Distance traveled by Eddie = Distance traveled by Eddie's sister
60(t - 5) = 50t
Step 5: Solve the equation for t.
60t - 300 = 50t
10t = 300
t = 30
Step 6: Calculate the distance between Eddie's home and the school.
Since t = 30 minutes, and Eddie's sister travels at an average speed of 50 m/min, the distance is
50 * 30 = 1500 meters.
Therefore, the distance between Eddie's home and the school is 1500 meters.