Question

Create a word problem for a linear equation, that has a constant rate of change

252

likes
1258 views

Answer to a math question Create a word problem for a linear equation, that has a constant rate of change

Expert avatar
Birdie
4.5
104 Answers
Sure! Here's a word problem that involves a linear equation with a constant rate of change:

Problem:
Alice is training for a marathon. On her first day of training, she runs for 30 minutes and covers a distance of 5 kilometers. Each week, she increases her training time by 10 minutes. Assuming that Alice maintains a constant rate of change in the distance she covers per minute, how far will she run in 60 minutes of training in her fourth week?

Solution:
To solve this problem, we need to find the constant rate of change in the distance covered per minute.

First, let's calculate the rate of change in the distance covered per minute on the first day:
Rate of change = Distance / Time = 5 km / 30 min = 1/6 km/min

Since Alice increases her training time by 10 minutes each week, we can find the total training time in the fourth week:
Total training time in the fourth week = 30 min + (10 min * 3 weeks) = 30 min + 30 min = 60 min

Now, we can use the constant rate of change to calculate the distance Alice will run in 60 minutes of training in her fourth week:
Distance = Rate of change * Time = (1/6 km/min) * 60 min = 10 km

Answer:
Alice will run a distance of 10 kilometers in 60 minutes of training in her fourth week.

Frequently asked questions (FAQs)
Math Question: What is the smallest positive integer solution for the equation x^n + y^n = z^n (
+
What is the sine of an angle when the opposite side is 3 and the hypotenuse is 5?
+
What is the equation of a circle with radius 5, centered at the point (2, -3)?
+
New questions in Mathematics
How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117
CASE 6-1: PREPARE A PRODUCTION PLAN: WHAT PROBLEMS ARRIVE? Midwest Plastics Company has conducted profit planning for several years. The president stated (with justification) that inventory control and planning had not been satisfactory, which was mainly due to poor planning of production and inventory budgets. Please analyze and provide recommendations, in detail, on the issue regarding the 20B profit plan, which is now being prepared. Their analysis and recommendations will be presented to the executive committee. Despite the seasonality factor, the sales department has been successful in developing a sales plan, on a monthly basis, for each year. The following sales data is available for 20B. 1. Sales plan summary for 20B: 2. Finished goods inventory, as of January 1, 20B, is 96,000 units. 3. Work-in-process inventory will remain constant. 4. Actual annual sales in 20A, including the estimate for December, were 350,000 units. 5. The average finished goods inventory during 20A was 70,000 units. IT IS REQUESTED. 1. Prepare the annual production budget, assuming that management policy is to budget ending finished goods inventory at a standard quantity, based on the ratio of historical sales of 20A to inventory turnover. 2. Prepare a schedule showing sales, production, and inventory levels for each month, assuming: 1) stable inventory, 2) stable production, and 3) recommended inventory-production levels. In developing your recommendations, assume that the following policies have been established: a) The president has set the policy that a maximum inventory of 85,000 units and a minimum inventory of 75,000 units should be used, except in abnormal circumstances. b) A stable level of production is definitely preferred, except that during the holiday season in July and August, production may be reduced by 25 percent. Likewise, a variation in production of 7.5 percent above and below the average level is acceptable. 3. What are the main problems faced by the company in production planning? Make your general recommendations.
STUDENTS IN A CLASS LEARN ONLY ONE FOREIGN LANGUAGE. two-sevenths of the students learn German, half of the students learn Spanish, and the remaining six students learn Italian. what is the number of students in this class? detail your reasoning carefully.
4.2x10^_6 convert to standard notation
The sum of two numbers is 6, and the sum of their squares is 28. Find these numbers exactly
Find the root of x^4-10x^ 5=0 using Newton's method, with a precision of the smallest positive root.
(3x^(2) 9x 6)/(5x^(2)-20)
Suppose the horses in a large they will have a mean way of 818 pounds in a variance of 3481. What is the probability that the mean weight of the sample of horses with differ from the population mean by more than 18 pounds is 34 horses are sampled at random from the stable.
To make brine, JosΓ© buys 1 kg of salt and pays 12 pesos. If he buys 4 kg, they charge him 48 pesos, but for 100 pesos they sell him 9 kg. What is the constant of proportionality?
There are 162 students enrolled in the basic mathematics course. If the number of women is 8 times the number of men, how many women are there in the basic mathematics course?
Determine the general equation of the straight line that passes through the point P (2;-3) and is parallel to the straight line with the equation 5x – 2y 1 = 0:
Your grandfather has run a small high street pharmacy for 40 years. After much persuasion, he has agreed to open a digital store online. List 5 potential ways to improve sales and/or margins by having a digital pharmacy through the utilisation of historic or new sales data.
Find the number of pounds of nails required for 17850 square feet of drywall if each thousand square feet requires 4.5 pounds of nails.
Let X be a discrete random variable such that E(X)=3 and V(X)=5. Let π‘Œ = 2𝑋^2 βˆ’ 3𝑋. Determine E(Y).
Determine the Linear function whose graph passes through the points (6, -2) and has slope 3.
Find the area of a triangle ABC when m<C = 14 degrees, a = 5.7 miles, and b = 9.3 miles.
The area bounded by the curve y=ln(x) and the lines x=1 and x=4 above the xβˆ’axis is
2.3 X 0.8
a coffee shop has 9 types of creamer and 11 types of sweetener. In how any ways can a person make their coffee?
Determine the general solution of the equation yβ€²+y=eβˆ’x .