a>you take a trip to visit your cousin. by 10;15 am the train has traveled 20 mi. by 10;30am the train has traveled an additional 15 mi. you are now half way to your cousins town.
1) if the trains rate is constant, what is its rate?
2) at what time will you reach your cousins town?
You've traveled 35 miles in 30 minutes.
The train must be averaging 70 mph.
so what time will they reach cousins town?
is it at 11am?
Right.
To find the rate of the train and the time you will reach your cousin's town, we need to use the formula:
Rate = Distance / Time
Let's calculate the answers to your questions step by step.
1) To find the rate of the train:
We know that by 10:15 am, the train has traveled 20 miles. By 10:30 am, it has traveled an additional 15 miles. So, the total distance traveled by the train is 20 + 15 = 35 miles.
To find the rate, we need to know the time it took to travel this distance. From 10:15 am to 10:30 am, 15 minutes have passed.
Now, we can calculate the rate:
Rate = Distance / Time
Rate = 35 miles / 15 minutes
To get the rate in miles per hour, we need to convert minutes to hours:
1 hour = 60 minutes
Rate = 35 miles / (15 minutes / 60 minutes per hour)
Rate = 35 miles / (15/60) hours
Rate = 35 miles / (0.25) hours
Rate = 35 miles / 0.25 hours
Rate = 140 miles per hour
So, the rate of the train is 140 miles per hour.
2) To find the time you will reach your cousin's town:
We know that you are halfway to your cousin's town when the train has traveled 35 miles. Since the distance to your cousin's town is twice the distance the train has traveled, we can calculate the total distance:
Total Distance = 2 * 35 miles
Total Distance = 70 miles
Now, we need to find the time it takes to travel this distance at the rate of 140 miles per hour:
Time = Distance / Rate
Time = 70 miles / 140 miles per hour
Time = 0.5 hours
Since we want to find the time when you will reach your cousin's town from the starting time of 10:15 am, we need to add the travel time of 0.5 hours:
Time = 10:15 am + 0.5 hours
Time = 10:45 am
So, you will reach your cousin's town at 10:45 am.