A man rides out into the country at a uniform rate of 30 miles per hour. He rests 2 hours and
then rides back at 20 miles per hour. He is gone 5 hours. How far did he go?

Question

A man rides out into the country at a uniform rate of 30 miles per hour.  He rests 2 hours and 
then rides back at 20 miles per hour.  He is gone 5 hours.  How far did he go?

anonymous · Answer

assume he rides out for x hours. then he rests for 2 hours, then he rides back for t hours.

so x + 2 + t = 5

it's important to note the distance riding out and riding back is the same. and that distance is given by speed * time = 30x = 20t

hence 20t = 30x hence t = 3x/2

thus x + 2 + 3x/2 = 5

thus x + 3x/2 = 3

thus 5x/2 = 3

thus 5x = 6 thus x = 6/5

thus the distance he travelled out was 30x = 36 miles