Problems of the Week – January 14 to January 18

Click here ^[1] for the Problem Extension Worksheet version of the Problems of the Week.
Click here ^[2] for an MS Word version of the Problems of the Week.
Click here ^[3] for the Canadian Problem Extension Worksheet version of the Problems of the Week.
Click here ^[4] for a Canadian MS Word version of the Problems of the Week.

^[5]Lower Elementary:
Question: On Monday, Rob sends a letter to Bailey at 10:00 AM. Bailey receives the letter at 1:30 PM on Wednesday. How many hours does it take for the letter to get from Rob to Bailey?
Answer: 51½ hours
Solution: After 10:00 AM, there are 14 hours left on Monday. The letter is in transit all 24 hours of Tuesday. 1:30 PM is 13½ hours into Wednesday. So, the letter takes 14 + 24 + 13½ = 51½ hours to get from Rob to Bailey.

^[6]Upper Elementary:
Question: Lina and Thomas are taking a vacation to San Francisco. Flights to San Francisco cost $250 per ticket. Return flights cost $325 per ticket. Lina and Thomas have a coupon for 50% off the cost of a single one-way ticket. What is the least they could spend on airfare before tax?
Answer: $987.50
Solution: To spend the least possible amount on their airfare, Lina and Thomas would need to use the coupon on one of the most expensive tickets. So, if they get 50% off a $325 ticket, one of those tickets is reduced to $325 ÷ 2 = $162.50. That means that the least Lina and Thomas could spend on airfare is $250 + $250 + $325 + $162.50 = $987.50.

^[7]Middle School:
Question: Roni and Taylor want to take a road trip. They need to save $1,000 to cover their costs. They have $400 left over from their last road trip. If Roni saves three times as much as Taylor by the time they have their $1,000, then how much money did Taylor save?
Answer: $150
Solution: Since Roni and Taylor already have $400, they need $1,000 – $400 = $600 more to reach their total. If Roni saves 3 times as much as Taylor, that means we need to split the remaining $600 into 4 equal parts—3 for Roni and 1 for Taylor. So, Taylor saves $600 ÷ 4 = $150.

^[8]Algebra and Up:
Question: Derek and Ben plan to meet for dinner at a fancy restaurant. Derek’s route to the restaurant is 4 miles, and his average driving speed en route is 20 miles per hour. Ben’s route to the restaurant is 6 miles, and his average driving speed en route is 24 miles per hour. If Derek starts driving to the restaurant 5 minutes after Ben, then who will reach the restaurant first? By how many minutes?
Answer: Ben arrives 2 minutes before Derek.
Solution: Derek drives at an average speed of 20 mph, so it takes him 20 mph ÷ 4 miles = of an hour = 12 minutes to drive to the restaurant. Ben drives at an average speed of 24 miles per hour, so it takes him 24 mph ÷ 6 miles = 15 minutes to drive to the restaurant. Since Derek starts driving 5 minutes after Ben, that means that Derek arrives 12 + 5 = 17 minutes after Ben starts driving. So, Derek arrives 2 minutes after Ben.