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WORD PROBLEMS REVIEW MATH 125
1.- A homeowner has installed an in-ground spa in the backyard. The spa is rectangular in shape, with a
length that is 4 feet more than its width. The homeowner put a one-foot-wide concrete border around
the spa. If the area covered by the spa and the border is 96 square feet, find the dimensions of the spa.
2.- A model rocket is launched from a platform that is 256 feet above the ground with an initial velocity
of 96 feet per second. The height of the rocket after t seconds is given by the function ℎ 𝑡 = −16𝑡 2 +
96𝑡 + 256. A) How long it will take the rocket to hit the ground? b) How long it take to reach the
maximum height? What is the maximum height?
3.- Find the length of the shorter leg of a triangle if the longer leg is 10 miles more than the shorter leg
and the hypotenuse is 10 miles less than twice the shorter leg.
4.- Johnny has $6.75 in dimes and quarters. He has 8 more dimes than quarters. How many quarters
does Johnny have? How many dimes does Johnny have?
5.- A deck for a home is in the shape of a triangle. The length of the base of the triangle is 9 feet longer
that its altitude. If the area of the triangle is 68 square feet, find the length of the base.
6.- A swimming pool can be emptied in 6 hours using a 10-horsepower pump along with a 6-horsepower
pump. The 6-horsepower pump requires 5 hours more than the 10- horsepower pump to empty the
pool when working by itself. How long would it take to empty the pool using just the 10-horsepower
pump?
7.- A plane flies 600 miles west (into the wind) and makes the return trip following the same flight path.
The effect of the jet stream on the plane is 15 miles per hour. The round trip takes 9 hours. What is the
speed of the plane in still air?
8.- With a tailwind, a small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the Piper
can fly the same distance in 4 hours. Find the average wind speed and the average airspeed of the Piper.
9.- A coffee distributor is blending a new coffee that will cost $3.90 per pound. It will consist of a blend
of $3.00 per-pound coffee and $6.00-per pound coffee. What amounts of each type of coffee should be
mixed to make 10 pounds of the blend?
10.-The kinetic energy K of a moving object varies jointly with its mass and square of velocity v.
If an object weighing 25 kilograms and moving with a velocity of 10 meters per second has a
kinetic energy 1250 joules, find its kinetic energy of the same object when the velocity is 15
meters per second.
11.- Suppose that you deposit $3,000 into a Roth IRA today. Determine the future value A of the
deposit if it earns 8% interest compounded quarterly after (a) 1 year, (b) 10 years, (c) 35 years, when
you plan on retiring.
Word Problems Answer key
1.- width 6ft. Length 10ft.
2.- It will take 8 seconds to hit the ground. The maximum height is 400 ft after 3 seconds.
3. The length of the shorter leg is 30 miles.
4.- 17 quarters and 25 dimes.
5.- The base is 17 ft.
6.- 10 hours
7.- 135 mph
8.- Plane’s speed is 175mph; wind speed is 25mph
9.- 7 pounds of $3.00 and 3 pounds of $6
10.- 2812.5 joules
11.- (a) $3,243 (b) 6,624.12 (c) $47, 989.40