SOLUTION: At 10:00 a.m. Samuel leaves his office traveling by car to deliver roses to Jennifer.He stopped to eat lunch for two hours,and then returned directly to his office,arriving at 2:00

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At 10:00 a.m. Samuel leaves his office traveling by car to deliver roses to Jennifer.He stopped to eat lunch for two hours,and then returned directly to his office,arriving at 2:00p.m. If Samuel rate going was 60 mph and the rate returning was 20 mph,how far is it from Samuel office to Jennifer's?
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Does the 20 mph include the 2 hours at lunch?

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Samuel was out of the office for 4 hours. Since he spent 2 hours to have lunch (with Jenny or somebody else), he was traveling for 2 hours to and from Jennifer's office.
 
Let's use ratio and proportions here. It is important to get how long each trip lasted. This would be easier if he were traveling in the same speed because we can easily say that it took him the same time to cover the distance to and from his destination. Since this is not the case, let's use logic.
 
If he travels faster to J's office, it would take him less time than when he traveled from J's office at a slower speed. Since he traveled three times faster to J's office, he would travel for one third of the time it takes him going back to his office. So we have this equation, where n is the time it takes him to go back to his office:
 



 
Therefore the trip to Jennifer's office took 1/2 hour. Traveling 60mph, we can get the distance by:
 
Distance = Rate x Time = 60 x = 30 miles.
 
Jennifer's office is 30 miles away.