The document contains multiple word problems involving linear equations with one unknown. The problems cover a range of topics including train speeds, plane speeds accounting for wind, mixing solutions of different concentrations, coin values, investment returns, filling pools, properties of triangles, rectangle areas, digit sums, and numbers with reversed digits.

1. Word Problems
Linear with One Unknown

2. There are two numbers whose sum is 50. Three times the first is
5 more than twice the second. What are the numbers?
Let x = first number
50-x = second number

3. There are two numbers whose sum is 72. One number
is twice the other. What are the numbers?

4. Abigail is 6 years older than Jonathan. Six years ago she
was twice as old as he. How old is each now?

5. A freight train starts from Los Angeles and heads for Chicago at
40 mph. Two hours later a passenger train leaves the same
station for Chicago traveling 60 mph. How long before the
passenger train overtakes the freight train?

6. A freight train starts from Los Angeles and heads for Chicago at
40 mph. Two hours later a passenger train leaves the same
station for Chicago traveling 60 mph How long before the
passenger train overtakes the freight train?.

7. A freight train starts from Los Angeles and heads for Chicago at
40 mph. Two hours later a passenger train leaves the same
station for Chicago traveling 60 mph How long before the
passenger train overtakes the freight train?.

8. 1
4
11
A plane takes 5 hours to fly from Los Angeles to Honolulu and
hours to return from Honolulu to Los Angeles. If the wind velocity
is 50 mph from the West on both trips, what is the airspeed of
the plane? (Airspeed is the speed of the plane in still air.)

9. 1
4
11
A plane takes 5 hours to fly from Los Angeles to Honolulu and
hours to return from Honolulu to Los Angeles. If the wind velocity
is 50 mph from the West on both trips, what is the airspeed of
the plane? (Airspeed is the speed of the plane in still air.)

10. 1
4
11
A plane takes 5 hours to fly from Los Angeles to Honolulu and
hours to return from Honolulu to Los Angeles. If the wind velocity
is 50 mph from the West on both trips, what is the airspeed of
the plane? (Airspeed is the speed of the plane in still air.)

11. 1
4
11
A plane takes 5 hours to fly from Los Angeles to Honolulu and
hours to return from Honolulu to Los Angeles. If the wind velocity
is 50 mph from the West on both trips, what is the airspeed of
the plane? (Airspeed is the speed of the plane in still air.)

12. In his motorboat, a man can go downstream in 1 hour less time than he can go
upstream the same distance. If the current is 5 mph, how fast can he travel in still
water if it takes him 2 hours to travel upstream the given distance?

13. In his motorboat, a man can go downstream in 1 hour less time than he can go
upstream the same distance. If the current is 5 mph, how fast can he travel in still
water if it takes him 2 hours to travel upstream the given distance?

14. A mixture containing 6% boric acid is to be mixed with 2 quarts of a mixture
which is 15% boric acid in order to obtain a solution which is 12% boric acid.
How much of the 6% solution must be used?

15. A mixture containing 6% boric acid is to be mixed with 2 quarts of a mixture
which is 15% boric acid in order to obtain a solution which is 12% boric acid.
How much of the 6% solution must be used?

16. Michael has some coins in his pocket consisting of dimes, nickels,
and pennies. He has two more nickels than dimes, and three
times as many pennies as nickels. How many of each kind of
coins does he have if the total value is 52 cents?

17. Michael has some coins in his pocket consisting of dimes, nickels,
and pennies. He has two more nickels than dimes, and three
times as many pennies as nickels. How many of each kind of
coins does he have if the total value is 52 cents?

18. Mr. McGregor invested $10,000. Part of it he put in the bank at 5 percent
interest. The remainder he put in bonds which pay 1 9 percent yearly return.
How much did he invest in each vehicle if his yearly income from the two
investment was $660?

19. Mr. McGregor invested $10,000. Part of it he puti n the bank at 5 percent
interest. The remainder he put in bonds which pay 1 9 percent yearly return.
How much did he invest in each vehicle if his yearly income from the two
investment was $660?

20. Mr. McGregor invested $10,000. Part of it he puti n the bank at 5 percent
interest. The remainder he put in bonds which pay 1 9 percent yearly return.
How much did he invest in each vehicle if his yearly income from the two
investment was $660?

21. If John can type a paper in 5 hours and together he and Jim can type it in 2
hours, how long would it take Jim to type the same paper alone?
Let x = number of hours
for Jim to type alone

22. Two women paint a barn. Barbara can paint it alone in 5 days, Sara in 8
days. They start to paint it together, but after 2 days Sara gets bored
and Barbara finishes alone. How long does it take her to finish?
Let x = number of days for Barbara to finish the barn

23. Two women paint a barn. Barbara can paint it alone in 5 days, Sara in 8
days. They start to paint it together, but after 2 days Sara gets bored
and Barbara finishes alone. How long does it take her to finish?

24. A swimming pool can be filled by an inlet pipe in 10 hours and emptied
by an outlet pipe in 12 hours. One day the pool is empty and the
owner opens the inlet pipe to fill the pool. But he forgets to close the
outlet. With both pipes open, how long will it take to fill the pool?
Let x = the number of hours to fill the pool with both pipes
open

25. The first angle of a triangle is twice the second, and the third is 5
degrees larger than the first. Find the three angles.

26. The first angle of a triangle is twice the second, and the third is 5
degrees larger than the first. Find the three angles.

27. The length of one rectangle is two times the width. If the
length is decreased by 5 feet and the width is increased by 5
feet, the area is increased by 75 square feet. Find the
dimensions of the original rectangle.

28. The length of one rectangle is two times the width. If the
length is decreased by 5 feet and the width is increased by 5
feet, the area is increased by 75 square feet. Find the
dimensions of the original rectangle.

29. The tens digit of a certain number is 3 less than the units digit.
The sum of the digits is 11. What is the number?

30. The sum of the digits in a two-digit number is 12. If the digits are
reversed, the number is 18 greater than the original number. What is
the number?

31. The sum of the digits in a two-digit number is 12. If the digits are
reversed, the number is 18 greater than the original number. What is
the number?