Josh and Greg leave from the same place and travel the same route. Josh travels 2 hours and stops. Greg travels 5 hours at double Josh's rate. After five hours they are 256 miles apart. Find the rate and distance of each.
Let's assume Josh's rate is "x" miles per hour.
Since Josh travels for 2 hours, the distance he covers is 2x miles.
Since Greg travels at double Josh's rate, Greg's rate is 2x miles per hour.
Since Greg travels for 5 hours, the distance he covers is 5(2x) = 10x miles.
We know that after 5 hours they are 256 miles apart.
So, the distance covered by Josh (2x) plus the distance covered by Greg (10x) equals 256 miles:
2x + 10x = 256
Combining like terms, we get:
12x = 256
Dividing both sides by 12, we get:
x = 256/12
Simplifying, we find:
x = 21.33
So, Josh's rate is approximately 21.33 miles per hour.
Now, let's calculate the distance each person has traveled:
Josh's distance = 2x = 2 * 21.33 = 42.66 miles
Greg's distance = 10x = 10 * 21.33 = 213.33 miles
Therefore, Josh has traveled approximately 42.66 miles and Greg has traveled approximately 213.33 miles.
To find the rate and distance traveled by Josh and Greg, we can use a few basic equations:
Let's assume the rate at which Josh travels is represented by 'r' (in miles per hour).
Since Josh travels for 2 hours, his distance traveled is given by: distance_josh = 2 * r.
Greg's rate is double that of Josh, so Greg's rate is given by: rate_greg = 2r.
Greg travels for 5 hours, so his distance traveled is given by: distance_greg = 5 * rate_greg = 5 * 2r = 10r.
After 5 hours, the distance between them is 256 miles.
So, the total distance traveled by both Josh and Greg is: distance_josh + distance_greg = 2r + 10r = 12r.
Now we can set up an equation using the total distance:
12r = 256.
Dividing both sides of the equation by 12, we find:
r = 256 / 12 = 21.33 miles per hour (rounded to two decimal places). This represents Josh's rate.
To find the distance traveled by Josh and Greg:
distance_josh = 2 * r = 2 * 21.33 = 42.67 miles.
distance_greg = 10 * r = 10 * 21.33 = 213.33 miles.
Therefore, Josh traveled at a rate of approximately 21.33 miles per hour and covered a distance of approximately 42.67 miles.
Greg traveled at twice Josh's rate, which is approximately 42.67 miles per hour, and covered a distance of approximately 213.33 miles.
thank you, ir das REALLY useful
distance = speed * time
So, if Greg's speed is s, then Josh's speed is 2s.
Greg travels 256 miles farther, so
2s + 256 = 5(2s)