On a trip to griffith observatory, dave rode his bicycle six more than twice as many miles in the afternoon as in the morning. if the entire trip was 57 miles long, then how far did he ride in the morning and in the afternoon?

Dave rode his bicycle 17 miles in the morning

Dave rode his bicycle 40 miles in the afternoon

Step-by-step explanation:

* Lets study the information to solve the question

- Dave rod his bicycle in the morning and again in the afternoon

- Six more than twice as many miles in the afternoon as in the morning

  means the distance in the afternoon is 6 more than twice the distance

  in the morning

- The entire trip was 57 miles means the total distance in the morning

  and in the afternoon was 75

* To solve the question let the distance in the morning is x miles

∵ The distance in the morning = x miles

∵ The distance in the afternoon is 6 more than twice the distance

  in the morning

∴ The distance in the afternoon = 2x + 6 miles

∵ The distance in entire trip = 57 miles

- The distance in the morning and the distance in the afternoon = 57 miles

∴ x + (2x + 6) = 57 ⇒ simplify

∴ 3x + 6 = 57 ⇒ subtract 6 from both sides

∴ 3x = 51 ⇒ divide both sides by 3

∴ x = 17 miles

∵ The distance in the morning is x miles

∴ Dave rode his bicycle 17 miles in the morning

∵ The distance in the afternoon = 2x + 6 miles

- Substitute the value of x

∴ The distance in the afternoon = 2(17) + 6 = 34 + 6 = 40 miles

∴ Dave rode his bicycle 40 miles in the afternoon