Question 236349
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.