Bluebook SAT Test SAT Word Problems Practice 5

Question 1

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?

Accepted Answer

240 miles

Answer

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.

Question 2

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?

Accepted Answer

10 liters

Answer

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.

Question 3

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?

Accepted Answer

6 days

Answer

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.

Question 4

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?

Accepted Answer

18 pounds

Answer

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.

Question 5

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?

Accepted Answer

$4,500

Answer

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.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test SAT Word Problems Practice 5