Solution:
Remember, distance traveled is the rate times the time. (d = rt) Mrs. Cunningham will overtake Mr. Cunningham when they have traveled the same distance.
Mrs. Cunningham's equation will be:
[tex]d=\text{ }75t[/tex]Since he was traveling 3 hours longer, Mr. Cunningham's equation will be:
[tex]d=55(t+3)[/tex]If they travel the same distance, the equations can be set equal to each other:
[tex]\text{ }75t=55(t+3)[/tex]applying the distributive property, this is equivalent to:
[tex]\text{ }75t=55t\text{ +165}[/tex]this is equivalent to:
[tex]75t-55t\text{ = 165}[/tex]this is equivalent to:
[tex]20t\text{ = 165}[/tex]solving for t, we obtain:
[tex]t\text{ =}\frac{165}{20}=8.25[/tex]So that, we can conclude that the correct answer is:
It will take Mrs. Cunningham 8.25 hours to overtake her husband.
