Math Problems of the Week - Nov 7th

Lower Elementary:

Question: Katie leaves her house at 7 o’clock in the morning to get some exercise. She walks for 8 minutes, jogs for 15 minutes, and runs for 10 minutes. Then she walks for 17 minutes to get home again. What time does Katie get home?

Answer:  7:50 am

Solution:  Katie walks for 8 + 17 = 25 minutes, jogs for 15 minutes, and runs for 10 minutes. Altogether, she exercises for 25 + 15 + 10 = 50 minutes. Fifty minutes after 7 o’clock am is 7:50 am.

Upper Elementary:

Question: Kyle’s swimming speed is 3 meters in 2 seconds. How long will it take him to swim a full lap of a 100 meter swimming pool—from one side to the other and back again?

Answer:  2 minutes and 13 seconds

Solution:  A full lap is 100 × 2 = 200 meters. Since 200 ÷ 3 = 66²/₃, 3 meters goes into 200 meters 66²/₃ times. So, it’ll take a total of 66²/₃ × 2 = 133¹/₃ seconds, or 2 minutes and 13 seconds.

Middle School:

Question: Isabel has a bicycle with wheels that measure 28 inches in diameter. How far will the bicycle go if the wheels rotate 100 times? (Round π to 3.14 to solve this problem.)

Answer:  732 feet and 8 inches

Solution:  The circumference of the wheel is approximately equal to its diameter multiplied by rounded π: 28 inches × 3.14 = 87.92 inches. If the wheel rotates 100 times, it’ll go 87.92 × 100 = 8,792 inches. That’s the same as 732 feet and 8 inches.

Algebra and Up:

Question: On a piece of graph paper, graph the equation x + 3y = ^–6.

Answer:

Solution:  One way to solve this problem is to solve for points and connect them. Another way is to rewrite the equation in slope-intercept form (y = –¹/₃x – 2), then use the intercept and the slope to plot the points (0, ^–2) and (3, ^–3).

Thanks, check back next week for more!