MENU
❌
Home
Math Forum/Help
Problem Solver
Practice
Algebra
Geometry
Tests
College Math
History
Games
MAIN MENU
1 Grade
Adding and subtracting up to 10
Comparing numbers up to 10
Adding and subtracting up to 20
Addition and Subtraction within 20
2 Grade
Adding and Subtracting up to 100
Addition and Subtraction within 20
3 Grade
Addition and Subtraction within 1000
Multiplication up to 5
Multiplication Table
Rounding
Dividing
Perimeter
Addition, Multiplication, Division
4 Grade
Adding and Subtracting
Addition, Multiplication, Division
Equivalent Fractions
Divisibility by 2, 3, 4, 5, 9
Area of Squares and Rectangles
Fractions
Equivalent Fractions
Least Common Multiple
Adding and Subtracting
Fraction Multiplication and Division
Operations
Mixed Numbers
Decimals
Expressions
6 Grade
Percents
Signed Numbers
The Coordinate Plane
Equations
Expressions
Polynomials
Symplifying Expressions
Polynomial Vocabulary
Polynomial Expressions
Factoring
7 Grade
Angles
Inequalities
Linear Functions
8 Grade
Linear Functions
Systems of equations
Slope
Parametric Linear Equations
Word Problems
Exponents
Roots
Quadratic Equations
Quadratic Inequalities
Rational Inequalities
Vieta's Formulas
Progressions
Arithmetic Progressions
Geometric Progression
Progressions
Number Sequences
Reciprocal Equations
Logarithms
Logarithmic Expressions
Logarithmic Equations
Trigonometry
Trigonometry
Identities
Trigonometry
Extremal value problems
Numbers Classification
Geometry
Intercept Theorem
Slope
Law of Sines
Law of Cosines
Vectors
Probability
Limits of Functions
Properties of Triangles
Pythagorean Theorem
Matrices
Complex Numbers
Inverse Trigonometric Functions
Analytic Geometry
Analytic Geometry
Circle
Parabola
Ellipse
Conic sections
Polar coordinates
Integrals
Integrals
Integration by Parts
Home
Practice
Word Problems - Proportions, Speed & Time
Word Problems - Proportions, Speed & Time: Problems with Solutions
Problem 1 sent by Ksenia
The sum of three consecutive even numbers is 78. What are the numbers?
25, 26, 27
24, 26, 27
22, 26, 30
24, 26, 28
Solution:
Let the first number be А
Then the sеcond is: А + 2
Third is: A + 4
A + (A + 2) + (A + 4) = 78
3 ⋅ A=72
A = 72/3
A = 24
Answer: 24, 26, 28
Problem 2
Kayla climbs 60 steps in 40 seconds. At that rate, how many steps could she climb in 150 seconds?
Solution:
Let's calculate the steps she climbs per second: 60:40 = 1.5
So she climbs 1.5 steps per second.
For 150 seconds Kayla climb: 1.5 × 150 = 225
Problem 3
From January through June, 46200 immigrants applied for citizenship. During this same period last year, 120000 immigrants applied. What is the percentage of decrease?
Answer:
%
Solution:
The decrease of immigrants is 120000 - 46200 = 73800.
The percentage of decrease is
(73800/120000) * 100 = 61.5%
Problem 4 sent by Radostina Jeliaskova
A store sold cherries in the afternoon twice as many as in the morning. Throughout the day were sold 360 kg. How many kilograms were sold in the afternoon?
Solution:
Let's suppose that
х
kg. were sold in the morning.
2x
were sold in the afternoon.
x + 2x = 360 <=>
3x = 360 <=> x = 120.
In the afternoon were sold 2x = 240 kg.
Problem 5
Two cyclists leave at the same time from the same place on a circle. The first does a lap in 3 minutes and the other in 4 minutes. After how much time will they meet again at the starting point?
Solution:
Because they do complete laps, the time that passes until the meeting must be a multiple of 3 and 4. The least common multiple of 3 and 4 is 12, so they will meet at the starting point after 12 minutes.
Problem 6 sent by Zaki
We give the following information about a race hedge.
There are 10 hurdles. The distance between consecutive two lines (that is to say which follow) is 9.14 m. There are 13.72 m between the starting line and the first line and the last hurdle between 14.02 m and line arrival. Each hurdle measures 106 cm in height.
What is the length(in centimeters) of the track?
Answer:
cm.
Solution:
13.72 + (9.14 × 9) + 14.02 + [(106÷100) × 10] =
13.72 + 82.26 + 14.02 + 10.6 =
120.6m = 12060cm.
Problem 7
If you divide a number into 3 equal groups and then divide each group in half, you end up with 13. What number did you start with?
Solution:
Suppose the start number is
x
Division into 3 equal groups is: x/3, and then in half is (x/3)/2 = 13
x/6 = 13
x = 13 ⋅ 6 = 78
Problem 8
A car runs 375 km in 3 hours. What's the car's speed?
Solution:
375 ÷ 3 = 125
Problem 9
A train leaves from city A at 9:15 and arrives at city B at 10:35. If the speed of the train is 180 km/h, what's the distance between the two cities?
Solution:
The length of a travel is 1 hour and 20 minutes. In one hour, the train runs 180 km and in 20 minutes (1/3 of an hour), the train runs 1/3 of the 180 km. The distance between cities is 180 km + 60 km = 240 km.
Problem 10
Tim rides his bike to school and arrives in 15 minutes. If his speed is 8 m/s, what's the distance between the school and his home?
Answer:
km.
Solution:
15 minutes = 15 × 60 = 900 seconds. His speed is 8 m/s, the distance between the school and his home is 900 × 8 = 7200 m = 7.2 km
Problem 11
A cyclist climbs a hill with a length of 400 m with a speed of 7.2 km/h. When descending, the speed is two times greater. How much time is necessary for the cyclist to climb and descend the hill?
Answer:
seconds.
Solution:
7.2 km = 7200 m.
1 h = 3600 s.
The speed is 7200 m/3600 s = 2 m/s. The necessary time to climb is 400 ÷ 2 = 200 seconds. When descending, if the speed is two times greater, the necessary time will be two times smaller, so 100 seconds. The total necessary time is 200 + 100 = 300 seconds.
Problem 12
The distance between 2 subway stations is 4.5 km. If the train leaves at 9:10 from one station and its speed is 90 km/h, what time does it get to the next station?
Answer format: hh:mm
Solution:
If the speed is 90 km/h, in a minute, the train will run 1.5 km. Thus, the necessary time to reach the next station will be 3 minutes, so the train arrives at 9:13.
Problem 13
A car runs the distance between cities A and B in 3 hours and 30 minutes with a speed of 180 km/h. A motorcyclist runs the same distance in 5 hours. What's the speed of the motorcycle?
Solution:
The distance between cities is 180 × 3 + 90 km = 630 km. Thus, the speed of the motorcyclist is 630 ÷ 5 = 126 km/h
Problem 14
The distance between 2 cities is 1200 km. A car runs a quarter of the way with a speed of 80 km/h and the rest with a speed of 120 km/h. How much time is necessary to run the whole distance?
Solution:
A quarter of 1200 is 1200 ÷ 4 = 300. The car runs this distance in 300 ÷ 80 = 3.75 hours = 3 hours and 45 minutes. The rest of 900 km are run in 900 ÷ 120 = 7.5 hours = 7 hours and 30 minutes. The total time will be 3 hours and 45 minutes + 7 hours and 30 minutes = 10 hours and 75 minutes = 11 hours and 15 minutes.
Problem 15
Joe and John are planning to paint a house together. John thinks that if he worked alone, it would take him 3 times more than if he worked with Joe to paint the whole house. Working together, they complete the job in $24$ hours. How long would it take each of them, working alone, to finish the job?
$12$ hours
$20$ hours
$32$ hours
$48$ hours
Solution:
Let $x$ be the time it takes Joe to complete the job.
$3x$ is the time it takes John to complete the job.
The speed of Joe: $\frac{1}{x}$
The speed of John: $\frac{1}{3x}$
The expression to represent the speed of each person using the formula $W=rt$, The amount of work done $(W)$ is the product of the speed of work $(r)$ and the time needed to do it $(t)$.
So $r=\frac{W}{t}$ then combined speed: $\frac{1}{x}+\frac{1}{3x}$ and since $1day=24hours$
$1=\left( \frac{1}{x}+\frac{1}{3x}\right) 24$ and now we can obtain $x$ so
$1=\left( \frac{3+1}{3x}\right) 24=\frac{96}{3x}=\frac{32}{x}\Longrightarrow x=32$
It takes $32$ hours for Joe to paint the house by himself and it takes $96$ hours for John to paint the house by himself.
Submit a problem on this page.
Problem text:
Solution:
Answer:
Your name(if you would like to be published):
E-mail(you will be notified when the problem is published)
Notes
: use [tex][/tex] (as in the forum if you would like to use latex).
Correct:
Wrong:
Unsolved problems:
Contact email:
Follow us on
Twitter
Facebook
Author
Copyright © 2005 - 2020.