greg traveled from his work at an average rate of 25km/hr. By traveling 50km/hr, he took 30 minutes less to return home. how far in kilometers is his work to home?
since time = distance/speed,
x/50 = x/25 - 1/2
To solve this problem, we can use the formula: Distance = Speed × Time.
Let's consider the distance from work to home as "d" km.
On the way to work:
Distance = Speed × Time
d = 25 × t1 --------(1)
On the way back home:
Distance = Speed × Time
d = 50 × t2 --------(2)
According to the given information, traveling at 50 km/hr took 30 minutes less than traveling at 25 km/hr.
We know that time = distance / speed. Therefore, we have:
t2 = t1 - 30/60 = t1 - 1/2
By substituting the value of t2 in equation (2), we can find the value of t1:
d = 50 × (t1 - 1/2)
d = 50t1 - 25 --------(3)
Now, equate equations (1) and (3) to find the value of d:
25t1 = 50t1 - 25
25t1 - 50t1 = -25
-25t1 = -25
t1 = 1
Substituting t1 = 1 into equation (1):
d = 25 × 1
d = 25 km
Therefore, the distance between Greg's work and home is 25 kilometers.
To find the distance between Greg's work and home, we need to use the concept of average speed and the given information.
Let's assume the distance between his work and home is 'd' kilometers.
We are given that Greg traveled from his work at an average rate of 25 km/hr, so the time it took him to reach home can be calculated as:
Time = Distance / Speed = d / 25 (in hours) ----(1)
We are also given that by traveling at 50 km/hr, he took 30 minutes (0.5 hours) less to return home. So, the time it took him to return home can be calculated as:
Time = Distance / Speed = d / 50 (in hours) ----(2)
The difference in time taken to return home can be written as:
d / 25 - d / 50 = 0.5 hours
To solve this equation, we can multiply both sides by 50 to eliminate the denominators:
2d - d = 0.5 * 50
d = 25 kilometers
Therefore, the distance between Greg's work and home is 25 kilometers.