Question 124730
Wilma drove at an average speed of 50 mi/h from her home in City A to visit her sister in City B. She stayed in City B 10 hours, and on the trip back averaged 45 mi/h. She returned home 40 hours after leaving. How many miles is City A from City B
:
First of all, let's just concern ourselves with the traveling time:
Subtract the 10 hr stay from the total time (40 hr) she was gone;
She had 30 hrs on the road
:
Let d = distance from A to B
:
Write a time equation: Time = {{{distance/speed}}}
:
Time to B + time to A = 30 hrs
{{{d/50}}} + {{{d/45}}} = 30
:
Multiply equation by a multiple of both denominators, 450 would do it: 
450*{{{d/50}}} + 450*{{{d/45}}} = 450(30)
Cancel out the denominators and you have:
:
9d + 10d = 13500
:
19d = 13500
d = {{{13500/19}}}
d = 710.5 miles from A to B
:
:
Check solution by finding the time each way and finding the total time:
710.5/50 = 14.2 hrs
710.5/45 = 15.8 hrs
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Total time 30.0 hrs as given
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Did I make this understandable? Any questions?