2. An express and local train leave Gray’s Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train.
Whatever you tried to cut and paste will have to be typed. Try again
To find the speed of each train, we can use the formula:
Speed = Distance / Time
Let's assign variables for the speed of the local train and the speed of the express train.
Let's say the speed of the local train is x miles per hour.
Then, the speed of the express train is 2x miles per hour (since it travels twice as fast).
Now, let's calculate the time it takes for each train to travel 50 miles.
For the local train:
Time = Distance / Speed = 50 miles / x mph
For the express train:
Time = Distance / Speed = 50 miles / (2x) mph
We know that the express train arrives 1 hour ahead of the local train. So, the time for the express train will be 1 hour less than the time for the local train.
50 miles / (2x) mph = (50 miles / x mph) - 1 hour
To solve this equation, we need to eliminate the hours from the equation. We know that 1 hour is equal to 60 minutes. So, we can convert the equation to minutes:
50 miles / (2x) mph = (50 miles / x mph) - 60 minutes
Now, let's solve the equation:
Cross-multiply:
50 miles * x mph = (50 miles * 2x mph) - (60 minutes * x mph)
Simplify:
50x = 100x - 60x
Combine like terms:
50x = 40x
Subtract 40x from both sides:
10x = 0
Divide both sides by 10:
x = 0
This tells us that the speed of the local train is 0 mph, which is not possible. It means there is a mistake somewhere in the problem or the information provided.
Please double-check the problem statement and make sure all the given information is accurate.