A cyclist's speed is 1.5 times faster than a walker's speed. They simultaneously start moving in the same direction from the same point, and after 1.5 hours, the distance between them is 12.5 miles. What are their speeds?
Let's assume the speed of the walker is x mph.
So, the speed of the cyclist is 1.5x mph.
Distance covered by the walker in 1.5 hours = x * 1.5 = 1.5x miles
Distance covered by the cyclist in 1.5 hours = 1.5x * 1.5 = 2.25x miles
The distance between them after 1.5 hours is 12.5 miles, so we can write the equation:
2.25x - 1.5x = 12.5
0.75x = 12.5
x = 12.5 / 0.75
x = 16.667
Therefore, the speed of the walker is approximately 16.667 mph.
And the speed of the cyclist is 1.5 * 16.667 = 25 mph.
Please try again
Let's assume the speed of the walker is x mph.
So, the speed of the cyclist is 1.5x mph.
Distance covered by the walker in 1.5 hours = x * 1.5 = 1.5x miles
Distance covered by the cyclist in 1.5 hours = 1.5x * 1.5 = 2.25x miles
The distance between them after 1.5 hours is 12.5 miles, so we can write the equation:
2.25x - 1.5x = 12.5
0.75x = 12.5
x = 12.5 / 0.75
x = 16.6667
Therefore, the speed of the walker is approximately 16.6667 mph.
And the speed of the cyclist is 1.5 * 16.6667 = 25 mph.
A train leaves LA at 2 pm, heading north at 50 mph. If the next train leaves three hours later and heads north at 60 mph, what time will the second train catch up to the first?
To solve this problem, we first need to determine how far the first train has traveled when the second train starts.
The first train travels for 3 hours at a speed of 50 mph, so the distance it covers is 50 mph * 3 hours = 150 miles.
Now, let's say the second train catches up to the first train after t hours.
During that time, the first train has been traveling for a total of (t + 3) hours and has covered a distance of 50 mph * (t + 3) hours = 50t + 150 miles.
The second train travels at a speed of 60 mph, so the distance it covers in t hours is 60 mph * t hours = 60t miles.
Since the second train catches up to the first train, the distances covered by both trains must be equal. Therefore, we can set up the equation:
50t + 150 = 60t
Subtracting 50t from both sides of the equation gives: 150 = 10t
Dividing both sides of the equation by 10 gives: t = 15
Therefore, the second train catches up to the first train after 15 hours.
To determine the time at which the second train catches up to the first, we add the 15 hours to the time the second train leaves, which is 2 PM + 3 hours = 5 PM.
Therefore, the second train catches up to the first train at 5 PM.
No
I apologize for the confusion. Let's solve the problem correctly.
The first train has a head start of 50 mph * 3 hours = 150 miles.
Now, let's consider the time it takes for the second train to catch up to the first train.
Relative to the second train, the first train is already ahead by 150 miles.
The second train travels at a speed of 60 mph, and the relative distance it needs to cover to catch up to the first train is 150 miles.
Using the formula for distance (distance = speed * time), we can set up the equation:
150 miles = 60 mph * t
Simplifying, we get:
150 miles = 60t
Dividing both sides by 60, we find:
t = 150 miles / 60 mph = 2.5 hours
Therefore, it will take the second train 2.5 hours to catch up to the first train.
To find the time at which the second train catches up, we add 2.5 hours to the departure time of the second train.
The second train departs at 2 PM + 3 hours = 5 PM.
Adding 2.5 hours, we find that the second train catches up to the first train at:
5 PM + 2.5 hours = 7:30 PM.
Therefore, the second train will catch up to the first train at 7:30 PM.
It's an AM!
I apologize for the mistake. Let's correct the answer.
The second train departs at 2 PM + 3 hours = 5 PM.
Adding 2.5 hours, we find that the second train catches up to the first train at:
5 PM + 2.5 hours = 7:30 PM.
Therefore, the second train will catch up to the first train at 7:30 PM.