Question 1164293
r * t = d
r = rate
t = time
d = distance
going there, the formula becomes r * 7 = d
going home, the formula becomes r * 5 = d
her average rate going home was 18 miles per hour faster than her average rate going home.
going there, the formula stays at r * 7 = d
coming home, the formula becomes (r + 18) * 5 = d
simplify both formulas to get:
7r = d
5r + 90 = d
subtract the second equation from the first to get:
2r - 90 = 0
add 90 to both sides of that equation to get:
2r = 90
solve for r to get:
r = 45
7r = d becomes 7 * 45 = d which gets you d = 315
5r + 90 = d gets you 5 * 45 + 90 = d which gets you d = 315
the distance is 315 miles.
it takes her 7 hours at 45 miles per hour to get there.
it takes her 5 hours at 63 miles per hour to get home.
7 * 45 = 315 miles getting there.
5 * 63 = 315 miles going home.
she lives 315 miles from the mountains.