problem library

There are 480 calories per hour. An officer swims 1.5 hours for 30 days. How many calories is that? 1.5 hours per day times 30 days = 45 total hours. 480 calories per hour times 45 total hours = 21,600 total calories.

At the end of the day, a bakery had 1/2 of a pie left over. The 4 employees each took home the same amount of leftover pie. How much pie did each employee take home? We have 1/2 of the pie eaten, if 1/2 was left over. So 1/2 of a pie divided by 4 employees = 1/8 of a pie per person. To check...

Two mechanics worked on a car. the first mechanic worked for 5 hours snd the second mechanic worked for 15 hours. Together they charged a total of $2375. What was the rate charged per hour by each mechanic if the sum of the two rates was $235 per hour? Setup equations where x is the rate of the...

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel? Each ride will cost 1.50 + 0.8x where x is the number of miles per trip. This expression...

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse is 6 years older than Alex. The sum of their ages is 31 years. How old is each one of them? Set up the relational equations where a = Alex's age, c = Chris's aged and j = Jesse's age a = c + 5 j...

Lena purchased a prepaid phone card for $15. Long distance calls cost 24 cents a minute using this card. Lena used her card only once to make a long distance call. If the remaining credit on her card is $4.92, how many minutes did her call last? Figure out how many minutes Lena used: Lena...

The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number by 18. What is the number? Let x and (16-x) represent the original ten and units digits respectively Reversing its digits increases the number by 18 Set up the relational equation [10x +...

Sound travels about 340 m/s. The function d(t) = 340t give the distance d(t),in meters., that sound travel in T seconds. How far goes sound traveling 59s? What we want is d(59) d(59) = 340m/s(59s) = 20,060m

If f(x) = 3x + 1 and g(x) = x^2 + 2x, find x when f(g(x)) = 10 Evaluate f(g(x)) f(g(x)) = 3(x^2 + 2x) + 1 f(g(x)) = 3x^2 + 6x + 1 When f(g(x)) = 10, we have 10 = 3x^2 + 6x + 1 Subtract 10 from each side: 3x^2 + 6x - 9 = 0 Divide each side of the equation by 3 x^2 + 2x - 3 = 0 Factor, we...

I HAVE $11.60, all dimes and quarters, in my pocket. I have 32 more dimes than quarters. how many dimes, and how many quarters do i have? Let d = dimes and q = quarters. We have two equations: 0.10d + 0.25q = 11.60 d - q = 32 Set up a system of equations to solve for d and q. dimes (d) = 56...

An ancient Greek was said to have lived 1/4 of his live as a boy, 1/5 as a youth, 1/3 as a man, and spent the last 13 years as an old man. How old was he when he died? Set up his life equation per time lived as a boy, youth, man, and old man 1/4 + 1/5 + 1/3 + x = 1. Using our LCM Calculator...

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is running at 5 feet per second and Claire is running at 3 feet per second. i. After how many seconds will Sophie catch Claire? ii. If the race is 500 feet, who wins? i. Sophie's distance formula...

Lucy has taken four tests in math class and has an average of 85. i. What score would she have to get on her fifth test to have an average of 88? ii. Can she get an average of 90? Explain. i. She would need a perfect score of 100 from our Missing Average Calculator ii. Impossible since we...

Take a look at the following sums: 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = 25 a. Come up with a conjecture about the sum when you add the first <i>n</i> odd numbers. For example, when you added the first 5 odd numbers (1 + 3 + 5 + 7 + 9), what did you get? What...

Julia has a bucket of water that weighs 10lbs. The total weight is 99% water. She leaves the bucket outside overnight and some of the water evaporates, in the morning the water is only 98% of the total weight. What is the new weight? Setup the proportion: 0.99/10 = 0.98/w Using our...

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD. If AB = 6 and AD = 8, by the Pythagorean theorem, we have BD = 10 from our Pythagorean Theorem Calculator Using that, we have another right triangle which we can use the pythagorean theorem...

Jack and Jill have a magic pail of beans. The number of beans in the pail doubles every second. If the pail is full after 10 seconds, when was the pail half full? Explain your answer. At time 0, we have n beans At time 1, we have 2n beans At time 2, we have 4n beans At time 3, we have 8n...

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over all the containers of eggs. Though she is unhurt, every egg is broken. So she goes to her insurance agent, who asks her how many eggs she had. She says she doesn't know, but she remembers...

A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and walked back to the starting point along the same path. She walks 4mph on level ground, 3 mph uphill, and 6 mph downhill. Find the distance she walked. Hint: Think about d = rt, which means...

Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What could N be? Is there more than one answer? For example, for 23 P(23) = 6 and S(23) = 5, but...