Question 1190897
rate * time = distance
for sam jogging:
rate * time = distance becomes 8 * x = distance
x = the time it took him to get to larry's home.
for sam riding back on larry's scooter:
rate * time = distance becomes 20 * y = distance.
y = the time it took him to get home.
your original two equations are:
8 * x = distance
20 * y = distance
the total time for the round trip was 7 hours.
this means that x + y = 7
solve for y to get:
y = 7 - x
the equations becomes:
for sam jogging:
8 * x = distance
for sam riding larry's scooter:
20 * (7 - x) = distance
your two equations are now:
8 * x = distance
20 * (7 - x) = distance
simplify the second equation and leave the first equation as is to get:
8 * x = distance
140 - 20 * x = distance
since distance = 8 * x in the first equation, replace distance with that in the second equation to get:
140 - 20 * x = 8 * x
add 20 * x to both sides to get:
140 = 28 * x
divide both sides by 28 to get:
5 = x
since x + y = 7, then y must be equal to 2.
your two original equations were:
8 * x = distance
20 * y = distance
replace x with 5 and y with 2 to get:
8 * 5 = 40
20 * 2 = 40
the distance is equal to 40 miles each way.
that would be a total of 80 miles round trip.
if you had added the distances together, then the round trip equation would have been:
8 * x + 20 * y = 80
with x = 5 and y = 2, the equation would have bvecome:
8 * 5 + 20 * 2 = 80
simplify to get:
40 +  40 = 80 which becomes 80 = 80, confirming the values of x and y are good.