SOLUTION: Here is the problem that I am having trouble explaining to my son. Scott and Dan are traveling together. First Scott drives one fifth of the way. Then Dan drives one third of t

Question 244123: Here is the problem that I am having trouble explaining to my son.
Scott and Dan are traveling together. First Scott drives one fifth of the way. Then Dan drives one third of the remaining distance. Next Scott drives one half of the remaining distance, and finally Dan drives the last 80 miles. What is the total distance traveled? How far does each person drive.
I know the answer is 300 miles total drive. Scott drove 140 and Dan drove 160.
I don't know how to explain the answer.
Can you help?
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Scott and Dan are traveling together. First Scott drives one fifth of the way. Then Dan drives one third of the remaining distance. Next Scott drives one half of the remaining distance, and finally Dan drives the last 80 miles. What is the total distance traveled? How far does each person drive.
--------------------
After Scott drives 1/5, 4/5 is left.
After Dan drive 1/3, 2/3 of 4/5 is left = 8/15 left.
Scott then drives half of that, so 4/15 is left, and is 80 miles.
Total = 80/(4/15) = 300 miles.
---------
Knowing the total, you can find the distances.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The first thing I have to say is that there is absolutely nothing wrong with the way Alan did this problem. I'm going to look at it from a slightly different direction, then you can choose the one you understand the best.

If Dan drove the final 80 miles, and that was what was left over after Scott had driven half of the remaining distance, then Scott must have driven 80 miles. Score: Dan 80, Scott 80, Total 160.

If Dan drove one-third of the remaining distance and left 160 miles to go, 160 must have been two-thirds of what remained when Dan started, so if 160 is two-thirds, 80 must be one-third, which is the amount Dan drove that leg. Score:

Dan 160, Scott 80, Total 240.

Next, if Scott drove one-fifth of the total trip and left 240 miles to go, then 240 miles must be four-fifths of the total trip. Dividing 240 by 4 gives 60 which is then one-fifth of the total trip and is what Scott drove at the start. Final Score: Dan 160, Scott 140, Total 300.

John

RELATED QUESTIONS
a. Mike and Scott live 110 miles from each other. They frequently meet for lunch at a... (answered by josmiceli)
Hi - I'm in seventh grade and this is my first time here. I'm having problems with a word (answered by sudhanshu_kmr)
Miss Scott said 'The sum of my current age and my age 20 years ago is equal to my age in... (answered by josgarithmetic)
I having problems simplifying fractions. I am totally lost, I don't understand where I... (answered by KMST,rothauserc)
Scott and Laura have both invested some money. Scott invested $3,000 more than Laura and... (answered by stanbon)
Hi, I am trying to help my daugther, but I am having trouble explaining the problem... (answered by checkley75)
I am having trouble getting to the point of a final answer. I am able to solve the Margin (answered by rothauserc)
I am working on Inequalities and I'm having trouble on a couple problems and the... (answered by Smirnov)