Please review the solutions to the previous week's problems. Then, move on to this set. Meanwhile, be looking at the marathon problems and providing solutions to some of them.
1. Isabella can paint a house in just 2 hours. Amy can paint a house in 200 hours (because she takes breaks to read and sip lemonade :-)). Working together, how long will it take them to paint 2 houses?
2. Amy is playing with her choo-choo train. Every 5 seconds, she giggles, and every 8 seconds, she claps her hands with glee. After what percent of a minute does Amy clap her hands and giggle at the same time?
3. Amy received a little conductor doll for her choo-choo train. She placed it on top of the train and then watched excitedly as it fell off the train and got squished under the wheels. Suddenly, it hit her that her conductor was dead, and she began to cry with pure anguish. Isabella, famous detective, was called in to investigate the cause of the conductor's death. The conductor was a flat rectangle and Isabella drew a chalk rectangle that exactly matched up with the conductor's plastic body. If the perimeter of the rectangle was 14 centimeters, and the product of the length and width is 10, what is the length and width?
4. Isabella came over to Amy’s house to play with her choo-choo train set. Unfortunately, Amy slipped on an ice cube and broke the set. They then divided up the work into two halves: Amy would find the pieces and Isabella would put them back together. It takes 3 hours for Amy to find a piece and 4.5 hours for Isabella to put it in its right spot. If the train set has 5000 pieces, how long will they be working?
HAPPY PROBLEM SOLVING!
1) 396
ReplyDelete2) about 67%
3) l=5
w=2
4) 37,500
Nidhi, well done! Check your work for problems 1 and 4, then repost your answers. Let me know if you need any hints.
ReplyDeletePlease take a look at the marathon problem.
ReplyDelete3) l = 5
ReplyDeletew = 2
4) 37,500
1) 404
ReplyDelete2) about 67%
3) l=5, w=2
Can I have a hint for #4?
Vishal and Nidhi, please post your approach to problem 4. This way, I'll try to catch the mistake in your reasoning.
ReplyDelete2. 67%
ReplyDelete3. l = 5 ; w=2
Good job, Avanthika! Keep trying problems 1 and 4.
ReplyDeleteNidhi, please post your problem for the marathon. Let's keep it running!
1. not sure
ReplyDelete2. about 67%
3. l=5, w=2
4.22,500
1) 404
ReplyDelete2) about 67%
3) l=5, w=2
4) 22,500....maybe...I dunno.
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ReplyDelete1) 404
ReplyDelete2) 67%
Nidhi, please post your problem on the marathon.
ReplyDeleteEveryone, take it as an opportunity when you are given the chance to post a problem on the marathon. It's meaningless if I post a problem on the marathon, because I've been posting sets here every week, or more than that if needed.
Making an effort to search for a problem and then posting it will help you sharpen up your math skills, and the marathon is for that sole purpose.
Please take your responsibility to post a problem when you are entitled to. Thanks and have fun!
Sorry for the delay guys! My problem is on the marathon now.
ReplyDeleteSolutions
ReplyDelete1. 1/2 + 1/200 = 101/200
1/(101/200) = 200/101 hours
2. The first meeting time occurs at 40 seconds = 2/3 of a minute = 66.666… %
3. 2 × (L + W) = 14
L × W = 10
Solving, we have L = 5 and W = 2.
4. It takes 4.5 × 5000 = 22500 hours total for Isabella. We add 3 because Amy has to find a piece before Isabella starts. Hence, we have 22500 + 3 = 22503 hours before they finish fixing the train set.