Question 236349: Jimmi needs to be home by 6 o団lock. If he travels at an average rate of 15mph, he値l arrive one hour early, but if he travels at an average rate of 10mph, he値l arrive one hour late, How many miles away is his home?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
r = rate
h = time
d = distance
formula becomes:
r*h = d
if we assume h is the right number of hours, then (h-1) gets him there too early and (h+1) gets him there too late.
we'll want to solve for h.
at 15 miles per hour he gets home 1 hour early.
15*(h-1) = d
at 10 miles per hour he gets home 1 hour late.
10*(h+1) = d
since they both equal the same distance, then they are equal to each other so we get:
15*(h-1) = 10*(h+1)
remove parentheses to get:
15h - 15 = 10h + 10
subtract 10h and add 15 to both sides of the equation to get
15h - 10h = 10 + 15
simplify to get
5h = 25
divide both sides by 5 to get:
h = 5
substitute h = 5 in both original equations to get:
15*(h-1) = d
10*(h+1) = d
become:
15*4 = d
10*6 = d
these equations become:
60 = d
60 = d
looks like the distance is 60 miles.
at 15 miles per hour he gets there in 4 hours which is 1 hour too early.
at 10 miles per hour he gets there in 6 hours which is 1 hour too late.
5 hours is just right which means he should be traveling at 12 miles per hour because 5 * 12 = 60.
you answer is:
the distance is 60 miles.
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