Bill drives his car 10 mph faster on the way home from work than he does going to work in rush hour. If it takes him 1 hrs. going and half an hour returning, how far away is his work?
Speed = r mi/h going to work.
Speed = (r+10)m/h returning.
d = r mi/h * 1 h = (r+10)mi/h * 0.5h
r * 1 = (r+10) * 0.5
r = 0.5r + 5
0.5r = 5
r = 10 mi/h
r+10 = 10+10 = 20 mi/h
d = 10 * 1 = (10+10) * 0.5 = 10 mi.
To determine the distance of Bill's work, we need to find the speed at which he drives during rush hour and on the way back.
Let's assume that Bill's speed during rush hour is "x" mph. According to the given information, his speed on the way home is 10 mph faster, which means his speed on the way home is (x + 10) mph.
We also know that it takes Bill 1 hour to drive to work and half an hour to return.
Using the formula: distance = speed * time, we can formulate the following equations:
Distance on the way to work = x mph * 1 hour
Distance on the way back from work = (x + 10) mph * 0.5 hours
Since the distances to and from work are the same, we have the equation:
x mph * 1 hour = (x + 10) mph * 0.5 hours
Simplifying the equation:
x = (x + 10) / 0.5
2x = x + 10
x = 10
So, Bill's speed during rush hour is 10 mph.
To find the distance of his work, we can substitute this value back into the distance formula:
Distance = 10 mph * 1 hour
Therefore, the distance of Bill's work is 10 miles.