Two travelers were 225 miles apart at 2:00 pm and were headed toward each other. If they met at 4:15pm and one was traveling 20 miles per hour faster than the other, what was the speed of each traveler?
To find the speeds of the two travelers, we can use the formula:
Distance = Speed × Time
Let's suppose the speed of the first traveler is x miles per hour. The speed of the second traveler would be x + 20 miles per hour, as it is 20 miles per hour faster.
Now, let's calculate the time traveled by each traveler. The total time traveled is 4 hours and 15 minutes, which is equivalent to 4.25 hours.
First Traveler:
Distance = Speed × Time
Distance = x × 4.25
Second Traveler:
Distance = Speed × Time
Distance = (x + 20) × 4.25
Since they met, the sum of their distances should equal the total distance between them, which is 225 miles.
x × 4.25 + (x + 20) × 4.25 = 225
Simplifying the equation:
4.25x + 4.25(x + 20) = 225
4.25x + 4.25x + 85 = 225
8.5x + 85 = 225
8.5x = 225 - 85
8.5x = 140
Now, we can solve for x:
x = 140 / 8.5
x ≈ 16.47
Therefore, the speed of the first traveler is approximately 16.47 miles per hour.
To find the speed of the second traveler, we add 20 miles per hour to the speed of the first traveler:
16.47 + 20 ≈ 36.47
So, the speed of the second traveler is approximately 36.47 miles per hour.
To find the speed of each traveler, we need to set up an equation based on the given information.
Let's assume the speed of one traveler is "x" miles per hour. Since the other traveler is going 20 miles per hour faster, their speed would be "x + 20" miles per hour.
We know that the two travelers met at 4:15pm, which is 2 hours and 15 minutes after 2:00pm. In terms of time, this is equivalent to 2.25 hours.
During this time, one traveler traveled at a speed of "x" miles per hour for 2.25 hours, which would be a distance of 2.25x miles.
The other traveler traveled at a speed of "x + 20" miles per hour for the same 2.25 hours, covering a distance of 2.25(x + 20) miles.
Since they were 225 miles apart when they met, the sum of the distances traveled by both travelers should equal 225 miles.
So, we can write the equation:
2.25x + 2.25(x + 20) = 225
Now, we can solve this equation to find the value of x, which will give us the speed of the first traveler.
they traveled 2.25 hours and covered 225 miles. So, their combined speed was 100 mi/hr.
60+40 = 100