SAT Word Problems Practice Flashcards

A train travels from City A to City B at an average speed of 80 mph. Due to track maintenance, it returns at an average speed of 60 mph. If the total round trip takes 7 hours, what is the one-way distance between the two cities?

Answer: 240 miles

Let d = one-way distance. Time A→B = d/80 and time B→A = d/60. Setting up the equation: d/80 + d/60 = 7. Using a common denominator of 240: 3d/240 + 4d/240 = 7, so 7d/240 = 7, giving d = 240 miles.

A chemist has 40 liters of a 25% acid solution. How many liters of pure acid must be added to produce a solution that is 40% acid?

Answer: 10 liters

Initial acid content = 0.25 × 40 = 10 liters. Let x = liters of pure acid added. The equation becomes (10 + x)/(40 + x) = 0.40. Solving: 10 + x = 16 + 0.4x → 0.6x = 6 → x = 10 liters.

Workers A and B together can complete a project in 8 days. Worker A alone can complete it in 12 days. If Worker B works alone for 6 days and then Worker A joins, how many additional days does it take to finish the project?

Answer: 6 days

Worker B's rate = 1/8 − 1/12 = 3/24 − 2/24 = 1/24 of the project per day. After 6 days alone, B completes 6/24 = 1/4 of the project. Remaining work = 3/4. Together their rate = 1/8 per day. Time to finish = (3/4) ÷ (1/8) = 6 additional days.

A coffee shop creates a 30-pound blend using Type X beans at $12/lb and Type Y beans at $18/lb. The blend is priced at $15.60/lb. How many pounds of Type Y beans are in the blend?

Answer: 18 pounds

Let y = pounds of Type Y. Then (30 − y) = pounds of Type X. Equation: 12(30 − y) + 18y = 15.60 × 30. Expanding: 360 − 12y + 18y = 468 → 6y = 108 → y = 18 pounds.

Marcus invests $8,000 total across two accounts. One earns 3.5% annual simple interest and the other earns 5% annual simple interest. After one year, the combined interest is $347.50. How much did Marcus invest in the 5% account?

Answer: $4,500

Let x = amount in the 5% account, so (8000 − x) is in the 3.5% account. Equation: 0.05x + 0.035(8000 − x) = 347.50. Expanding: 0.05x + 280 − 0.035x = 347.50 → 0.015x = 67.50 → x = $4,500.

A rectangular garden has a perimeter of 84 feet. The length is 6 feet more than twice the width. What is the area of the garden in square feet?

Answer: 360 sq ft

Let w = width. Then length = 2w + 6. Using perimeter: 2(w + 2w + 6) = 84 → 2(3w + 6) = 84 → 6w + 12 = 84 → 6w = 72 → w = 12 ft. Length = 2(12) + 6 = 30 ft. Area = 12 × 30 = 360 sq ft.