Question

The Cunninghams are moving across the country. Mr.Cunningham leaves 3 hours before Mrs. Cunningham. If he averages 55 mph and sheaverages 75 mph, how many hours will it take Mrs. Cunningham to catch up to Mr. Cunninham to catch up to mr.cunningham

Answer 1

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:

`d=\text{ }75t`

Since he was traveling 3 hours longer, Mr. Cunningham's equation will be:

`d=55(t+3)`

If they travel the same distance, the equations can be set equal to each other:

`\text{ }75t=55(t+3)`

applying the distributive property, this is equivalent to:

`\text{ }75t=55t\text{ +165}`

this is equivalent to:

`75t-55t\text{ = 165}`

this is equivalent to:

`20t\text{ = 165}`

solving for t, we obtain:

`t\text{ =}(165)/(20)=8.25`

So that, we can conclude that the correct answer is:

It will take Mrs. Cunningham 8.25 hours to overtake her husband.