Gabe lives fifteen miles from school and the bus stops seven times at three minutes each between his house and school. The bus arrives at his house at 7:30. Gabe's friend Aaron lives 8 miles from school and the bus stops four times at 2 minutes each between his house and school. The bus arrives at his house at 8:00. What time does each boy arrive at school?
Can someone please help? I have no idea how to turn this into an equation; it seems so long and confusing.
|TimeGabe= leaving time + stopping time
Time Aaron= leaving time + stopping time.
I still don't get it! My brain is burnt right now.
TimeGabe=leaving time + stopping time
7:51=7:30 + 21(7x3)
Gabe arrives @ 7:51, right?
Then for Aaron:
Time Aaron=leaving time + stopping time
same thing:
8:08=8:00 + 8(4x2)
So Aaron gets there @ 8:08.
Thank you so much! :)
No problem!
=)brie
To solve this problem, we can start by calculating the total time it takes for each boy to travel to school, including the time spent waiting at the bus stops.
Let's break it down step by step:
1. Gabe's travel time:
- Distance from Gabe's house to school = 15 miles
- Number of bus stops = 7
- Time spent at each bus stop = 3 minutes
- Total time spent at bus stops = 7 stops * 3 minutes/stop = 21 minutes
To find the total travel time for Gabe, we need to add the time spent at bus stops to the time it takes to travel the distance between his house and school. We know from the problem that the bus arrives at Gabe's house at 7:30, so we can subtract this time from the total travel time to find when Gabe arrives at school.
2. Aaron's travel time:
- Distance from Aaron's house to school = 8 miles
- Number of bus stops = 4
- Time spent at each bus stop = 2 minutes
- Total time spent at bus stops = 4 stops * 2 minutes/stop = 8 minutes
Similar to Gabe's case, we need to add the time spent at bus stops to the time it takes to travel the distance between Aaron's house and school. The bus arrives at Aaron's house at 8:00, so we can subtract this time from the total travel time to find when Aaron arrives at school.
Let's calculate the arrival times for each boy step by step:
1. Gabe's arrival time:
- Total travel time for Gabe = Time to travel distance + Time spent at bus stops
- Time to travel distance = Distance / Speed (we need the speed of the bus to calculate this accurately, but the problem doesn't provide this information)
- For simplicity, let's assume a constant speed for the bus, say 30 mph (miles per hour)
- Time to travel distance = 15 miles / 30 mph = 0.5 hours = 30 minutes
- Total travel time for Gabe = 30 minutes + 21 minutes = 51 minutes
Given that the bus arrives at Gabe's house at 7:30, Gabe will arrive at school in 51 minutes. Adding this to 7:30, we get:
- Gabe's arrival time = 7:30 + 51 minutes = 8:21 AM
2. Aaron's arrival time:
- Total travel time for Aaron = Time to travel distance + Time spent at bus stops
- Time to travel distance = Distance / Speed (again, we'll assume a constant speed of 30 mph)
- Time to travel distance = 8 miles / 30 mph = 0.27 hours ≈ 16 minutes
- Total travel time for Aaron = 16 minutes + 8 minutes = 24 minutes
Given that the bus arrives at Aaron's house at 8:00, Aaron will arrive at school in 24 minutes. Adding this to 8:00, we get:
- Aaron's arrival time = 8:00 + 24 minutes = 8:24 AM
Therefore, Gabe arrives at school at 8:21 AM, and Aaron arrives at school at 8:24 AM.