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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.
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