D = r*t is the equation they give you
D = distance
r = rate (aka speed)
t = time
For Amanda, her equation is
D = 3.5*t
since she walks for t hours and does so at a speed of 3.5 mph
For Alexis, her equation is
D = 4*t
for similar reasons: she walks for t hours at 4 mph
Add up the two distances 3.5*t and 4*t
This sum must be equal to 4. Why 4? Because the total distance between the two houses is 4 miles. The two friends meet at some point between the houses. So Amanda's distance adds up with Alexis' distance to get the total.
We have this equation
3.5*t + 4*t = 4
Solve for t
3.5*t + 4*t = 4
(3.5+4)*t = 4
7.5*t = 4
7.5*t/7.5 = 4/7.5
t = 4/7.5
t = 0.53333 (this is approximate; the 3s go on forever)
Rounding to the nearest hundredth (2 decimal places) we get t = 0.53
So it takes roughly 0.53 hours for the two friends to meet which is the final answer
Note: 0.53 hours is equal to 31.8 minutes
Another note: due to rounding errors, the true time in minutes should be 32 since (4/7.5)*60 = 32. However, the teacher wants the answer in hours (not minutes). So the answer is still 0.53
