A car leaves a city at 70 km/hr. After 15 minutes, another car follows at 80 km/h. How long will it take for the second car to reach the first, and at what distance?
First, make sure all units are compatible:
Convert 15 minutes to hours, since the speeds are listed in km per hour.
15 minutes / 60 min/hr = .25 hours
Set up algebra equations:
Then let x be the distance traveled by the car that travels at 70 km/hr
Let y be the distance traveled by the car that travels at 80 km/hr
Let t be the time
When the second car starts, the first car has already traveled 70 km/h * .25 h = 17.5 km
x = 17.5 + 70*t
y = 80 * t
The cars will meet when x = y, or when
80*t = 17.5 + 70*t
Solve for t, the time at which they meet. Plug back t into the equation for x or y to find the distance at which they meet.
To determine how long it will take for the second car to reach the first and at what distance, we need to analyze their relative speeds and the time it takes for the second car to catch up.
Given:
- First car's speed: 70 km/h
- Second car's speed: 80 km/h
Let's first convert the initial time (15 minutes) into hours:
15 minutes = 15/60 = 1/4 hour
Now, let's calculate how far the first car would travel during this time:
Distance = Speed x Time
Distance = 70 km/h x (1/4) hour
Distance = 17.5 km
So, after the first car travels for 15 minutes, it will be 17.5 km away from the starting point.
Next, let's find out the difference in speed between the two cars:
Relative Speed = Second car's speed - First car's speed
Relative Speed = 80 km/h - 70 km/h
Relative Speed = 10 km/h
Now, we can calculate the time it will take for the second car to close the initial distance of 17.5 km between them:
Time = Distance / Relative Speed
Time = 17.5 km / 10 km/h
Time = 1.75 hours
Thus, it will take the second car 1.75 hours to catch up to the first car.
To find the distance at this time, we can use the formula:
Distance = Speed x Time
Distance = 80 km/h x 1.75 hours
Distance = 140 km
Therefore, it will take the second car 1.75 hours to reach the first car, and at a distance of 140 km from the starting point.