A train leaves the station at noon.The train is 180 miles from its destination at 12:45pm,and 90 miles from its destination at 2:15p.m..At what time will the train reach the destination?
well, it traveled 90 miles in 1 1/2 hours.
So, it is still 1 1/2 hours away at 2:15
To solve this problem, we need to find the rate at which the train is traveling and then use that to determine the time it will take to reach the destination.
First, let's find the rate at which the train is traveling.
From 12:00 pm to 12:45 pm, the train traveled 180 miles. This means it traveled 180 miles in 45 minutes.
To find the rate, we can divide the distance by the time.
180 miles / 45 minutes = 4 miles per minute
Next, let's find the time it takes to travel 90 miles using the rate we found.
We know that the rate is 4 miles per minute, so we can use this information to set up the equation:
90 miles = 4 miles/minute * t minutes
To solve for t, divide both sides of the equation by 4 miles per minute:
90 miles / (4 miles/minute) = t
t = 22.5 minutes
Now, we have the time it takes to travel 90 miles: 22.5 minutes.
To find the total time from the start to the destination, we add up the time it took to travel the first 180 miles (45 minutes) and the time it took to travel the remaining 90 miles (22.5 minutes).
45 minutes + 22.5 minutes = 67.5 minutes
Therefore, the train will reach its destination 67.5 minutes after noon.
To convert this to hours, we divide by 60 (since there are 60 minutes in an hour):
67.5 minutes / 60 minutes/hour = 1.125 hours
Therefore, the train will reach its destination at approximately 1:08 pm (assuming it maintains a constant speed).