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Word Problems - Problems with Solutions
Problem 1 sent by Ksenia
The sum of three consecutive numbers is 78. What are the numbers?
Solution:
Let the first number be А
Then the socond 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:
(46200/120000) * 100 = 462/12 = 38.5
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 then
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]] => L = [13.72 + 82.26 + 14.02 + 10.6] =>L=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 20 seconds. When descending, if the speed is two times greater, the necessary time will be two times smaller, so 10 seconds. The total necessary time is 20 s + 10 s = 30 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.
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