Q: Two trains are 300 miles apart and travel towards each other on parallel tracks. Train A travels at 60 mph and Train B at 40 mph. At the same time, a bird starts flying from Train A towards Train B at 100 mph, turning around instantly each time it reaches a train. How far will the bird have flown by the time the trains meet?

$\displaystyle 200\ \text{miles}$

Q: A cylindrical water tank is 10 feet tall and has a circumference of 12 feet. If you want to wrap a rope around the tank 5 times from bottom to top, how much rope do you need?

$\displaystyle 5 \times 12 = 60\ \text{feet}$

Q: A rectangular garden is 30 feet long and 20 feet wide. You want to put a fence around it and also one straight line of fencing across the middle, parallel to the shorter side. How much fencing do you need?

$\displaystyle 2 \times (30 + 20) + 20 = 120\ \text{feet}$

Q: Juan is wrapping 8 turns of ribbon around each of 10 cylindrical posts, each 8 feet high with a circumference of 6 feet. How many feet of ribbon does he need in total?

$\displaystyle 8 \times 10 \times 6 = 480\ \text{feet}$

Q: A car leaves City X traveling at 50 mph. Two hours later, a second car leaves City X traveling at 70 mph in the same direction. How long after the second car leaves will it catch up to the first car?

$\displaystyle 3\ \text{hours}$

Q: Jordan and Amari run a 200-meter race. Jordan wins by 10 meters. If they race again and Jordan starts $d$ meters behind the starting line, what value of $d$ will make the race a tie?

$\displaystyle 10\ \text{meters}$ (since Jordan won by 10 meters, starting 10 meters behind will tie the race)

Q: A rectangular field is 100 meters long and 60 meters wide. If you want to build a path 2 meters wide all around the outside of the field, what is the area of the path?

$\displaystyle (104 \times 64) - (100 \times 60) = 1056\ \text{m}^2$

Q: A chemist needs to mix a 20% saline solution with a 50% saline solution to obtain 10 liters of a 30% saline solution. How many liters of the 20% solution should be used?

$\displaystyle 6.67\ \text{liters}$

Q: A company wants to build a rectangular parking lot with an area of $\displaystyle 2400\ \text{m}^2$. If the length must be 3 times the width, what are the dimensions of the lot?

$\displaystyle 60\ \text{m} \times 20\ \text{m}$

Q: A plane flies 600 miles with a tailwind in 2 hours and returns against the wind in 3 hours. What is the speed of the plane in still air?

$\displaystyle 250\ \text{mph}$

Question 1

Two trains are 300 miles apart and travel towards each other on parallel tracks. Train A travels at 60 mph and Train B at 40 mph. At the same time, a bird starts flying from Train A towards Train B at 100 mph, turning around instantly each time it reaches a train. How far will the bird have flown by the time the trains meet?

Accepted Answer

$\displaystyle 200\ 	ext{miles}$

Question 2

A cylindrical water tank is 10 feet tall and has a circumference of 12 feet. If you want to wrap a rope around the tank 5 times from bottom to top, how much rope do you need?

Accepted Answer

$\displaystyle 5 	imes 12 = 60\ 	ext{feet}$

Question 3

In a 400-meter race, Runner A finishes 20 meters ahead of Runner B. If they race again and Runner A starts 20 meters behind the starting line, assuming both run at the same pace as before, who will win the second race?

Accepted Answer

They will tie.

Question 4

A rectangular garden is 30 feet long and 20 feet wide. You want to put a fence around it and also one straight line of fencing across the middle, parallel to the shorter side. How much fencing do you need?

Accepted Answer

$\displaystyle 2 	imes (30 + 20) + 20 = 120\ 	ext{feet}$

Question 5

A cyclist travels from Town A to Town B, a distance of 60 miles, at 15 mph. On the return trip, due to wind, the cyclist travels at 10 mph. What is the cyclist's average speed for the entire trip?

Accepted Answer

$\displaystyle 12\ 	ext{mph}$

Question 6

Juan is wrapping 8 turns of ribbon around each of 10 cylindrical posts, each 8 feet high with a circumference of 6 feet. How many feet of ribbon does he need in total?

Accepted Answer

$\displaystyle 8 	imes 10 	imes 6 = 480\ 	ext{feet}$

Question 7

A car leaves City X traveling at 50 mph. Two hours later, a second car leaves City X traveling at 70 mph in the same direction. How long after the second car leaves will it catch up to the first car?

Accepted Answer

$\displaystyle 3\ 	ext{hours}$

Question 8

Jordan and Amari run a 200-meter race. Jordan wins by 10 meters. If they race again and Jordan starts $d$ meters behind the starting line, what value of $d$ will make the race a tie?

Accepted Answer

$\displaystyle 10\ 	ext{meters}$ (since Jordan won by 10 meters, starting 10 meters behind will tie the race)

Question 9

A rectangular field is 100 meters long and 60 meters wide. If you want to build a path 2 meters wide all around the outside of the field, what is the area of the path?

Accepted Answer

$\displaystyle (104 	imes 64) - (100 	imes 60) = 1056\ 	ext{m}^2$

Question 10

A chemist needs to mix a 20% saline solution with a 50% saline solution to obtain 10 liters of a 30% saline solution. How many liters of the 20% solution should be used?

Accepted Answer

$\displaystyle 6.67\ 	ext{liters}$

Question 11

A company wants to build a rectangular parking lot with an area of $\displaystyle 2400\ 	ext{m}^2$. If the length must be 3 times the width, what are the dimensions of the lot?

Accepted Answer

$\displaystyle 60\ 	ext{m} 	imes 20\ 	ext{m}$

Question 12

A plane flies 600 miles with a tailwind in 2 hours and returns against the wind in 3 hours. What is the speed of the plane in still air?

Accepted Answer

$\displaystyle 250\ 	ext{mph}$

Question 13

A rectangular swimming pool is 25 meters long and 10 meters wide. If you want to tile the border around the pool with a width of 1 meter, what is the area of the border?

Accepted Answer

$\displaystyle (27 	imes 12) - (25 	imes 10) = 324 - 250 = 74\ 	ext{m}^2$

Question 14

A store sells two types of coffee beans: one at $\displaystyle \$8$ per pound and another at $\displaystyle \$12$ per pound. How many pounds of each should be mixed to get 10 pounds of a blend worth $\displaystyle \$10$ per pound?

Accepted Answer

$\displaystyle 5\ 	ext{lb}$ of each

Question 15

A rectangular playground is to be fenced on all four sides. If the length is twice the width and the total perimeter is 180 meters, what are the dimensions of the playground?

Accepted Answer

$\displaystyle 60\ 	ext{m} 	imes 30\ 	ext{m}$

Question 16

A car rental company charges $\displaystyle \$30$ per day plus $\displaystyle \$0.20$ per mile. If you rent a car for 3 days and drive 150 miles, what is the total cost?

Accepted Answer

$\displaystyle 3 	imes 30 + 0.2 	imes 150 = 90 + 30 = \$120$

Question 17

A rectangular lot is 50 meters longer than it is wide. If the perimeter is 300 meters, what are the dimensions of the lot?

Accepted Answer

$\displaystyle 75\ 	ext{m} 	imes 25\ 	ext{m}$

Question 18

A 20-foot ladder leans against a wall. The foot of the ladder is 12 feet from the wall. How high up the wall does the ladder reach?

Accepted Answer

$\displaystyle 16\ 	ext{feet}$

Question 19

A rectangular parking lot has a length that is 4 meters more than its width. If the area is $\displaystyle 96\ 	ext{m}^2$, what are the dimensions of the lot?

Accepted Answer

$\displaystyle 12\ 	ext{m} 	imes 8\ 	ext{m}$

College Algebra Word Problem Guidance: Distance, Rate, and Geometry

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