answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lapatulllka
2 months ago
7

Ethan and Leo start riding their bikes at the opposite ends of a 65-mile bike path. After Ethan has ridden 1.5 hours and Leo has

ridden 2 hours, they meet on the path. Ethan’s speed is 6 miles per hour faster than Leo’s speed. Find the speed of the two bikers
Mathematics
1 answer:
Svet_ta [12.7K]2 months ago
6 0

Let Leo's speed be denoted as x miles per hour

therefore, Ethan's speed is (x + 6) miles per hour

Applying the formula Distance = Speed × Time

thus the distance Leo covers in 2 hours = x × 2 = 2x

and the distance that Ethan travels in 1.5 hours is 1.5( x + 6 ) = 1.5x + 9

given that they met on the route, after Ethan had cycled for 1.5 hours and Leo for 2 hours, together they covered the entire route measuring 65 miles.

⇒ distance traveled by Leo in 2 hours plus distance traveled by Ethan in 1.5 hours equals 65

⇒ 2x + 1.5x + 9 = 65

⇒ 3.5x = 56

⇒ x = 16

Therefore, Leo's speed is x miles/hr = 16 miles/hour

and Ethan's speed is (x + 6) miles/hr = 16 + 6 = 22 miles/hour

You might be interested in
Fifty-five percent of the members of the junior varsity swim team wear glasses. Of the team memebers who do not wear glasses, 30
tester [12383]
I believe the answer is d 67 or c 55 because it's the closest number.
4 0
1 month ago
Read 2 more answers
Juan builds this pedestal for a trophy. What is the volume of the pedestal? Enter your answer in the box. in³ Three-dimensional
Zina [12379]
The solution is negative 0
4 0
1 month ago
Elia rode her bicycle from her house to the beach at a constant speed of 18 kilometers per hour, and then rode from the beach to
Svet_ta [12734]

Answer:

Elia took \dfrac{5}{11} hour to cycle from her residence to the beach, \dfrac{6}{11} hour to return, and traveled

8\dfrac{2}{11} kilometers from her home to the beach and

8\dfrac{2}{11} kilometers on her way back.

Step-by-step explanation:

1. Let b represent the hours Elia spent cycling to the beach, and p the time taken for the return trip to the park. The combined time for both rides equals 1 hour, represented as

b + p = 1

2. With a constant speed of 18 km/h on her way to the beach, in b hours, she covered 18b kilometers. She then rode back from the beach to the park at a steady speed of 15 km/h, which amounted to 15p kilometers.

Since the distances for both trips are identical, we establish

18b = 15p

3. Solve the two equations:

\left\{\begin{array}{l}b+p=1\\ \\18b=15p\end{array}\right.

Using the first equation

b=1-p

Insert this solution into the second equation

18(1-p)=15p\\ \\18-18p=15p\\ \\18=18p+15p\\ \\33p=18\\ \\p=\dfrac{18}{33}=\dfrac{6}{11}\\ \\b=1-\dfrac{6}{11}=\dfrac{5}{11}

Elia took \dfrac{5}{11} hour to cycle to the beach, \dfrac{6}{11} hour on her return, and covered

18\cdot \dfrac{5}{11}=\dfrac{90}{11}=8\dfrac{2}{11} kilometers going to the beach and

15\cdot \dfrac{6}{11}=\dfrac{90}{11}=8\dfrac{2}{11} kilometers returning to her home.

5 0
3 months ago
Read 2 more answers
The test scores of 40 students are listed below. Find P 56. 30 35 43 44 47 48 54 55 56 57 59 62 63 65 66 68 69 69 71 72 72 73 74
zzz [12365]
Answer: 74
5 0
2 months ago
Which equations are equivalent to Three-fourths + m = negative StartFraction 7 over 4 EndFraction? Select three options. m = Sta
Zina [12379]
1) m = -10/4. 2) m = -5/2. 3) m = [Step-by-step extraction continues here]. The equation presented is: → [next steps, if applicable]. Subtracting 3/4 from both sides → m = [continues to final form].
5 0
2 months ago
Read 2 more answers
Other questions:
  • Which steps can be used to solve StartFraction 6 Over 7 EndFraction x + one-half = StartFraction 7 Over 8 EndFraction for x? Che
    9·2 answers
  • Marlene rides her bike at a rate of 16 miles per hour. The time in hours that she rides is represented by the variable t, and th
    13·2 answers
  • Which of the following scenarios best describes division of a polynomial using synthetic division? Select all that apply. The di
    13·1 answer
  • Describe two ways to solve the equation 2(4x-11)=10
    5·1 answer
  • Suppose that surface σ is parameterized by r(u,v)=⟨ucos(3v),usin(3v),v⟩, 0≤u≤7 and 0≤v≤2π3 and f(x,y,z)=x2+y2+z2. Set up the sur
    13·1 answer
  • The function f(x) = −x2 − 5x + 50 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in
    12·2 answers
  • At a school party there are 40 cookies. The ratio of chocolate cookies to oatmeal cookies is shown in the tape diagram. Chocolat
    5·2 answers
  • Item 15 A square wrestling mat has a perimeter of (12x−32)(12x−32) feet. Write an expression in simplest form that represents th
    8·1 answer
  • 11. In a certain town the ratio of the number of cars to that of taxis is 15:4. If
    5·2 answers
  • Nick used a $10 bill to pay for a picnic, which cost $p. ​How much change did Nick receive? If P = 4 what would the expression b
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!