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: A plane has 9 seats in each row. In the first row, there is a man sitting in the first seat, a woman in the second seat, and another man in the third seat. If this pattern repeats for the whole row, how many men are in the row?
Answer: 6 men
Solution: Let’s write out the pattern and complete it for the whole row. M = man, W = woman. M, W, M, M, W, M, M, W, M
Counting the number of Ms, we find there are 6 men in the row.
[6]Upper Elementary:
Question: A plane leaves New York at 10:30 am heading to California. If the flight is 5½ hours long, what time will it be in California when it lands? (New York is 3 hours ahead of California.)
Answer: 1:00 pm
Solution: One way to do this is to add 5½ hours to 10:30 am. Since ½ an hour is 30 minutes we add, 10:30 am + 5 hours + 30 minutes = 4:00 pm New York time. Since California is 3 hours behind New York it is, 4:00 pm − 3 hours = 1:00 pm in California when the plane lands.
[7]Middle School:
Question: The ratio of child to adult passengers on a plane is 15:16. There is a total of 217 passengers on the flight. How many passengers are adults?
Answer: 112 passengers are adults
Solution: Since we know the total number of passengers we need to find the ratio of adult passengers to total passengers. The ratio of child to adult is 15:16 making the ratio of adults to total number of passengers 16:31. Setting up the proportion, (16 adults)/(31 children+adults) = (x adults)/(217 children+adults) and solving for x, we get 112 adult passengers.
[8]Algebra and Up:
Question: It takes 3 hours for a plane to travel 1,740 miles with the wind. Flying against the wind, the plane can travel 1,410 miles in the same amount of time. What is the speed of the plane in still air? What is the speed of the wind?
Answer: plane speed = 525 mph, wind speed = 55 mph
Solution: Using D = RT, we can setup two equations. Let P = the speed of the plane in still air and W = the speed of the wind. Our equation with the wind is, 3(P + W) = 1,740 and against the wind is 3(P − W) = 1,410. Solving this system of equations
3 P + 3 W = 1,740
3 P − 3 W = 1,410
6 P = 3,150
we find P = 525 mph and W = 55mph.
2 Comments To "Problems of the Week – October 22 to October 26"
#1 Comment By Joshua Edgar On October 21, 2018 @ 12:52 pm
The problem of the week for lower elementary is a little um… problematic? The pattern could be correctly be assumed to continue M W M W M W M W M instead of the way shown above. This would result in a total of 5 Men and 4 Women.
#2 Comment By Melissa Sikorski On October 22, 2018 @ 1:56 pm
Hi Joshua, you are correct, by assuming the fourth person is a woman the pattern could be MW repeating. Since we don’t know if the fourth person is a woman based on the information given, we want the student to duplicate the given pattern, MWM, for the complete row of 9 people. In other words, “If this pattern (MWM) repeats for every group of 3 seats in the row, how many men are in the row?” I hope that makes more sense.