lantheman said:
On an exercise, a soldier marches for four days. On the first day, he covers 25% of the journey. On the second day, he covers one-third of the remaining distance, on the third, 25% of the remaining journey and, on the final day he covers half of the remaining distance. He still has 15 miles left to travel. How far has he walked in total?
Here is what I did:
15x2=30
30x4=120
120x3=360
360x4=1440
Total miles traveled = 1440 miles
This seems like too much
Where did I go wrong?
You've posted this twice here, and also have tried the "live help" room at another site.
Let's try working backwards.
On the last day, he walked HALF of the remaining distance, and there were still 15 miles left to go. So....how far did he walk that last day? There were 15 miles left, and that was half the distance at the beginning of the last day. SO...he must have walked 15 miles that last day, and when he started on that last day, 30 miles of the trip lay ahead of him.
Last day, he walked 15 miles.
Now, at the end of the third day, he had 30 miles left....and he had walked 25% of the remaining journey. So what he has left at the end of that day must be 75% (or 3/4) of the distance remaining at the beginning of the day. 30 is 3/4 of 40, right? So, he started the third day with 40 miles ahead of him, and he walked 10 miles during that day.
Third day, he walked 10 miles.
At the end of the second day, then, he still had 40 miles left. And on the second day, he'd walked 1/3 of the distance that lay ahead of him at the beginning of the second day. 40 miles must be 1 - 1/3, or 2/3 of the distance at the beginning of that second day. And if 40 miles is 2/3 of the distance, 1/3 of the distance must be 20 miles. That's how far he walked on the second day.
Second day, he walked 20 miles.
Ok....that means there must have been 60 miles facing him at the beginning of the second day. That was AFTER he walked 25% of the journey. So that 60 miles must be 75% (or 3/4) of the total trip.
You finish....
And yes, 1440 miles is much too much.
