Bobby didn't have any cookies, so he started buying 2 cookies per day. He didn't eat them, only collected them in a box. He used to collect stamps. We don't know why he decided to make the switch to something perishable.
Jen started out with 100 cookies and ate 3 every day. Apparently, she is a collector of calories. Delicious, delicious calories.
After how many days did Bobby and Jen have the same number of cookies?
Answer
20 days.
Example 2
Uncle Scrooge has 1 million dollars. If his nephew Huey starts with $1000 and makes $100 per day, how many years will it be until Huey has as much as Uncle Scrooge?
Answer
9,990 days, or about 27.4 years.
Example 3
Nick and Kevin went to climb a mountain, starting from sea level. They didn't care for each other, but their girlfriends insisted they spend some time together so they could bond. However, they never promised they would go up the mountain at the same time. Sneaky. Nick started climbing at noon and was 500 feet up by 1 p.m. Kevin started climbing at 12:15 p.m., and at 12:30 p.m. was 75 feet up the mountain. When did Kevin pass Nick?
Answer
Kevin didn't ever pass Nick. If x is the number of minutes that have passed since noon and y is feet, Nick's line is
and Kevin's line is
y = 5x – 75.
These lines intersect when x is negative, which doesn't make sense for this problem. How could Kevin pass Nick before they even started climbing? Don't think for a second that this was an accident or a mistake. They totally planned it that way.
Example 4
Jin and Li have offices on the same highway. Not on the actual highway. All their papers would blow away. They both work just off the same roadway, however.
At noon they leave their offices and drive towards a local restaurant where they have a lunch meeting. Jin's office is 40 miles east of the restaurant, while Li's office is only 20 miles east of the restaurant. What, there wasn't a Subway close by?
If Li gets to the restaurant at 12:20 p.m. and Jin gets there at 12:40 p.m., at what time do Li and Jin pass on the road?
Answer
Never. If x is minutes and y is miles, Li's line is
y = 20 – x,
while Jin's line is
y = 40 – x.
Since these lines have the same slope, they are parallel, so the system of equations is inconsistent. Since the lines never intersect, Li and Jin are never at the same place along the road. Not a bad thing. This way, there's no risk of them trying to drive alongside one another so they can wave and then getting into an accident.
Example 5
Aisha and Jojo each drove South on Route 1, heading for mile 0 in Key West, Florida. At 1 p.m., Aisha was 120 miles away from mile 0, driving 40 miles per hour all the way. Jojo was 112 miles away, and drove 28 miles per hour for the rest of the trip.
At what time did Aisha pass Jojo?
When did Aisha get to mile 0? When did Jojo get to mile 0?
Answer
1:40 p.m.
Aisha got there at 4 p.m., while Jojo got there at 5 p.m.
Example 6
Sandy sells seashells by the seashore. Lucy also sells seashells by the seashore, but her tongue-twister isn't so twisty. After one week of seashell selling, Lucy has 32 seashells left of her original 74, and Sandy has 34 left of her original 90. After how many days of seashell selling do Lucy and Sandy have the same number of seashells left?
