Question

Two cyclists start at the same point and travel in opposite directions. One cyclist travels 4 miles an hour slower than the other. If the two cyclists are 64 miles apart after 2 hours, what is the rate of each cyclist?

likes

293 views

Answer to a math question Two cyclists start at the same point and travel in opposite directions. One cyclist travels 4 miles an hour slower than the other. If the two cyclists are 64 miles apart after 2 hours, what is the rate of each cyclist?

$Expert avatar$

Neal

4.5

105 Answers

Let

be the speed of the faster cyclist in miles per hour. The slower cyclist's speed is then

x - 4

miles per hour.

In 2 hours, the distance travelled by the faster cyclist is:

\text{Distance}_{\text{fast}} = x \times 2

And the distance travelled by the slower cyclist is:

\text{Distance}_{\text{slow}} = (x - 4) \times 2

The total distance between them after 2 hours is 64 miles:

2x + 2(x - 4) = 64

Simplifying the equation:

2x + 2x - 8 = 64

4x - 8 = 64

4x = 72

x = 18

The speed of the faster cyclist is:

x = 18 \, \text{mph}

The speed of the slower cyclist is:

x - 4 = 18 - 4 = 14 \, \text{mph}

Thus, the rate of each cyclist is 14 mph and 18 mph.

Frequently asked questions (FAQs)

Find the period of the trigonometric function y = 3cos(5x) - 2sin(3x) + 1.

What is the radius (r) of a circle given the equation x^2 + y^2 = 25?

Question: What is the largest prime factor of the mixed number 3 1/4 when written as an improper fraction?

New questions in Mathematics

To calculate the probability that a player will receive the special card at least 2 times in 8 games, you can use the binomial distribution. The probability of receiving the special card in a single game is 1/4 (or 25%), and the probability of not receiving it is 3/4 (or 75%).

Let the vectors be u=(-1,0,2) , v=(0,2,-3) , w=(2,2,3) Calculate the following expressions a)<u,w> b) <2u- 5v,3w>

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.

two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?

Additionally, the boss asked Armando to determine how many toy sales branches he would have in the fifteenth year, knowing that the first year they started with two branches, by the second they already had 5 branches and, by the third year, they had 8 branches. From the above, determine the number of branches it will have for the fifteenth year.

The beta of a company is 1,41 and its cost of equity 18,95%. What is then the market risk premium if the risk free rate is 0,94%? (in %, 2 decimal places)

The mean life of a television set is 119 months with a standard deviation of 13 months. If a sample of 67 televisions is randomly selected, what is the probability that the sample mean would be less than 121 months? Round your answer to four decimal places

If the midpoint of point A on the x=3 line and point B on the y=-2 line is C(-2,0), what is the sum of the ordinate of point A and the abscissa of point B?

What is the total tolerance for a dimension from 1.996" to 2.026*?

In the telephone exchange of a certain university, calls come in at a rate of 5 every 2 minutes. Assuming a Poisson distribution, the average number of calls per second is: a) 1/8 b) 1/12 c) 1/10 d) 2/5 e) 1/24

A storage maker price is $2.50 per square feet. Find the price of a custom shed 4 yards long, and 5yards wide and 8 feet tall

Use the sample data and confidence level given below to complete parts (a) through (d). A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4336 patients treated with the drug, 194 developed the adverse reaction of nausea. Construct a 99% confidence interval for the proportion of adverse reactions.

There are 3 orchards, a, b and c. Orchard a has 60 fewer trees than orchard b orchard c has 3 times as many trees as orchard b. If the three orchards have 430 trees altogether, how many trees does orchard c have?

A Smooth Plane is listed for $195.00. Discounts of 12% and 10% are allowed. If the customer pays cash within 30 days, an additional discount of 3% is granted. What is the cost if a carpenter takes advantage of all the discounts offered?

2x2

Two particles of electrical charges Q1=3.8×10-⁶C and q,=4.4×10-⁶C are separated in vacuum by a distance of 4.0.10-⁸ m. Since K=9.0.10⁹ N.m²/C², the intensity of the interaction force between them, in newtons, is?

Calculate NPV, IRR and PAYBACK through a cash flow for a period of five years, with discount rate of: a) 10% b) 12% c) 15% initial annual cost $41,400,000

a coffee shop has 9 types of creamer and 11 types of sweetener. In how any ways can a person make their coffee?

Consider a sample space S, and two events A and B such that P(A ∩ B) = 0.2, P(A ∪ B) = 0.6, P(B ∪ ̄A) = 0.8 (a) [0.5 points] Calculate P (A). (b) [0.5 points] Calculation P (B)

The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?

Two cyclists start at the same point and travel in opposite directions. One cyclist travels 4 miles an hour slower than the other. If the two cyclists are 64 miles apart after 2 hours, what is the rate of each cyclist?

Answer to a math question Two cyclists start at the same point and travel in opposite directions. One cyclist travels 4 miles an hour slower than the other. If the two cyclists are 64 miles apart after 2 hours, what is the rate of each cyclist?

You might be interested in