This week's problems are below. Please complete them and also continue running the marathon. It will help you build better math skills.
Problems:
1. If 8 cars are worth 5 planes, and 4 planes are worth 9 boats, how many cars are worth 90 boats?
2. Two legs of a right triangle are 12 and 5. What is the length of the hypotenuse?
3. Alice and Bob live 22 miles apart along the only route between their houses. Alice begins riding her bicycle towards Bob's house, while Bob does the same after a while. Alice bicycled at 3/5 the rate Bob bicycled at. When the two met, Alice had been travelling twice as long as Bob had been. How far from Alice's house did they meet up?
4. To train for a marathon, Mei runs an 18-mile course at a constant speed. If she doubles her usual speed, she can complete the course in an hour and a half less than her usual time. What is Mei's usual speed and her usual time to complete the course?
5. Is 2011 a prime number? What numbers did you divide by before reaching to your conclusion?
1) 64 cars
ReplyDelete2) 13
3) 4.66 miles
4) Working on it
5) yes; 3,7,11,13,17,19,23,29,31,37,41,43
1. 64 cars=90 boats
ReplyDelete2. 13- I used the Pythagoras' Theorem.
3. I really don't get this, but 17.6?
4. Still doing it.
5. Yes, 2,3,5,7,11,13,17,19,23,29
Good job, guys! Happy Snow/Math day!!!
ReplyDeleteNeha and Vishal, keep working on problems 3 and 4. Neha, you missed out a few numbers on problem 5, check your answer with Vishal's.
You guys are building great math skills. Keep up the good work!
3) 44.66 miles
ReplyDelete4) working on it
Vishal, think about your answer to problem 3. If Alice and Bob live 22 miles apart, how could they meet at 44.66 miles from Alice's house if they met in between the 22-mile route? The answer should be less than 22 miles, right?
ReplyDeleteYou could use this formula to from a system of equations to solve the problem.
d = s × t
where s = speed, t = time, and d = distance traveled.
1. 64
ReplyDelete2. 13
3. 12 miles
4. time= 3hrs speed= 6m/h
5. Yes,3,7,11,13,17,19,23,29,31,37,41,43
Simran, great job! All your answers are correct.
ReplyDeleteEveryone, work on the marathon problems until I post the solutions to these problems and the new week's problems.
Sorry Agni I meant 14.66 miles apart.
ReplyDeleteSolutions
ReplyDelete1. 8 cars = 5 planes
9 boats = 4 planes
90 boats = ___ cars
We can say that 90 boats = 40 planes by multiplying the second equation by 2. 40 planes = 8 × 8 = 64 cars by the first equation.
2. Have a few basic Pythagorean Triples memorized, such as:
3-4-5
5-12-13
6-8-10
7-24-25
8-15-17
(Look to the MATHCOUNTS Toolbox for a reference with greater content.)
Hence, we have a 5-12-13 right triangle, with hypotenuse 13.
Alternatively, we could have used the Pythagorean Theorem.
5² + 12² = x²
x² = √169 = 13
3. The first step when solving these kinds of problems is to define variables. We can say that:
A = Alice's time
a = Alice's speed
B = Bob's time
b = Bob' speed
From what the problem tells us, we know that the distance Alice traveled can be denoted as:
(3/5)b × 2B
The distance that Bob traveled can be denoted as:
Bb
We know that [(3/5)b × 2B] + Bb = 22. Solving for Bb, we have:
(11Bb)/5 = 22
11Bb = 22 × 5 = 110
Bb = 10
Thus, the distance Alice traveled is 22 - 10 = 12 miles.
4. Let's call Mei's usual speed s and her usual time t.
Equation 1: st = 18
Equation 2: 2s(t - 1.5) = 18
We solve these equations for s and t. Equation 2 becomes:
2st - 3s = 18
We substitute 18 in for st and get:
3s = 18
s = 6
t = 3
5. 2011 is a prime number. We know this by testing all the prime numbers which are less than its square root: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, and 43.