Rate and Unit Word Problems
Help Questions
SSAT Upper Level: Quantitative › Rate and Unit Word Problems
A factory produces widgets at a rate of 150 widgets per hour. Due to a machine malfunction, the production rate decreases by 20% for 3 hours, then returns to normal. If the factory operates for 8 hours total, how many widgets are produced?
1080 widgets
960 widgets
1140 widgets
1200 widgets
Explanation
Normal rate: 150 widgets/hour. Reduced rate: 150 × 0.8 = 120 widgets/hour. Production for 3 hours at reduced rate: 3 × 120 = 360 widgets. Production for remaining 5 hours at normal rate: 5 × 150 = 750 widgets. Total: 360 + 750 = 1140 widgets.
Two cyclists start from the same point and travel in opposite directions. Cyclist A travels at 15 mph and Cyclist B travels at 18 mph. After how many minutes will they be exactly 11 miles apart?
18 minutes separation time
24 minutes separation time
22 minutes separation time
20 minutes separation time
Explanation
Combined rate of separation: 15 + 18 = 33 mph. Time to be 11 miles apart: 11 ÷ 33 = 1/3 hour = 20 minutes.
A recipe calls for ingredients to be mixed at a rate of 2 cups per 3 minutes. If a chef mixes for 15 minutes but takes a 2-minute break after every 5 minutes of mixing, what is the total amount mixed?
9 cups total amount mixed
12 cups total amount mixed
8 cups total amount mixed
10 cups total amount mixed
Explanation
The chef mixes for 5 minutes, breaks for 2 minutes, mixes for 5 more minutes, breaks for 2 minutes, then mixes for 5 final minutes. Total mixing time: 5 + 5 + 5 = 15 minutes (the breaks don't count toward mixing). Rate: 2 cups per 3 minutes = 2/3 cups per minute. Amount mixed: 15 × (2/3) = 10 cups.
A assembly line produces 240 units per hour. After 2 hours of operation, a quality control check takes 30 minutes, during which production stops. The line then resumes at 90% efficiency. If the total production target is 1560 units, how many total hours (including the quality control time) are needed?
6.5 total hours needed
8.0 total hours needed
7.0 total hours needed
7.5 total hours needed
Explanation
Units produced in first 2 hours: 240 × 2 = 480 units. Remaining units needed: 1560 - 480 = 1080 units. Production rate after check: 240 × 0.9 = 216 units/hour. Time for remaining units: 1080 ÷ 216 = 5 hours. Total time: 2 hours + 0.5 hours (check) + 5 hours = 7.5 hours.
A water tank is being filled by two pipes simultaneously. Pipe A fills the tank at 12 gallons per minute, while Pipe B fills it at 8 gallons per minute. After 15 minutes, Pipe A is shut off and only Pipe B continues filling. If the total time to fill the 400-gallon tank is 25 minutes, how many gallons were in the tank initially?
80 gallons initially present
20 gallons initially present
60 gallons initially present
40 gallons initially present
Explanation
Combined rate for first 15 minutes: 12 + 8 = 20 gal/min. Water added in first 15 minutes: 15 × 20 = 300 gallons. Water added in last 10 minutes (Pipe B only): 10 × 8 = 80 gallons. Total water added: 300 + 80 = 380 gallons. Initial amount: 400 - 380 = 20 gallons.
A car travels 180 miles in 3 hours. For the first hour, it travels at 50 mph. For the remaining distance, it maintains a constant speed. What is this constant speed for the last two hours?
60 miles per hour constant speed
70 miles per hour constant speed
75 miles per hour constant speed
65 miles per hour constant speed
Explanation
Distance in first hour: 50 × 1 = 50 miles. Remaining distance: 180 - 50 = 130 miles. Time for remaining distance: 3 - 1 = 2 hours. Speed for last two hours: 130 ÷ 2 = 65 mph.