Word Problem Parser Math Calculator
Solve distance-rate-time, percentage, ratio, work-rate and mixture word problems step by step by entering the known values for each problem type.
Formula
D=RT | Result=Base x P/100 | 1/T=1/T1+1/T2 | C1V1+C2V2=Cf(V1+V2)
Different word problem types use different formulas. Distance problems use D=RT. Percentage problems use Result = Base x Percent/100. Work rate problems use 1/T = 1/T1 + 1/T2. Mixture problems use conservation of substance: C1V1 + C2V2 = Cf(V1+V2). The solver identifies the type and applies the correct formula.
Worked Examples
Example 1: Distance-Rate-Time Problem
Problem:A train travels at 85 mph for 4.5 hours. How far does it travel?
Solution:Type: Distance problem Known: Rate = 85 mph, Time = 4.5 hours Unknown: Distance Formula: D = R x T D = 85 x 4.5 = 382.5 miles
Result:The train travels 382.5 miles
Example 2: Work Rate Problem
Problem:Pipe A fills a pool in 6 hours. Pipe B fills it in 4 hours. How long with both pipes?
Solution:Rate A: 1/6 pool per hour Rate B: 1/4 pool per hour Combined: 1/6 + 1/4 = 2/12 + 3/12 = 5/12 pool per hour Time = 1 / (5/12) = 12/5 = 2.4 hours
Result:Both pipes together fill the pool in 2.4 hours (2 hours 24 minutes)
Frequently Asked Questions
How do I identify what type of word problem I have?
Look for keyword clues in the problem text. Distance problems mention speed, rate, mph, travel, or time. Percentage problems use words like percent, discount, markup, tax, or tip. Ratio problems reference proportions, ratios, or comparisons. Work rate problems describe multiple workers or machines completing a task together. Mixture problems involve combining solutions, concentrations, or blending. Once you identify the type, you can select the appropriate formula template and plug in the known values to solve for the unknown.
What is the distance-rate-time formula?
The fundamental relationship is Distance = Rate x Time (D = RT). This can be rearranged to solve for any variable: Rate = Distance / Time, or Time = Distance / Rate. This formula applies to any constant-speed scenario including driving, walking, flying, or even data transfer rates. For problems with multiple legs at different speeds, calculate each segment separately and add the distances or times. The average speed for a multi-leg trip is total distance divided by total time, which is NOT the average of the individual speeds.
How do work rate problems differ from simple rate problems?
Work rate problems involve combining individual rates to find a joint completion time. The key insight is that rates are additive: if Worker A completes 1/5 of a job per hour and Worker B completes 1/3 per hour, together they complete 1/5 + 1/3 = 8/15 per hour, finishing in 15/8 = 1.875 hours. A common mistake is averaging the times (which would give 4 hours). Work rate problems appear in plumbing (pipes filling tanks), construction, manufacturing, and computing scenarios. The general formula extends to any number of workers: 1/T = 1/T1 + 1/T2 + ... + 1/Tn.
What are common percentage word problem patterns?
There are three fundamental percentage patterns: (1) Finding a percentage of a number: 'What is 25% of 80?' uses Result = Base x Percent/100. (2) Finding the percentage: '15 is what percent of 60?' uses Percent = (Part/Whole) x 100. (3) Finding the base: '30 is 40% of what?' uses Base = Part / (Percent/100). Real-world applications include sales tax, discounts, tips, interest, population growth, and test scores. Multi-step problems might chain these: 'A $240 jacket marked down 15%, then charged 6% tax' requires sequential calculation, applying each step to the running value rather than to the original price.
How do I solve mixture and concentration problems?
Mixture problems rely on the conservation principle: the total amount of pure substance before mixing equals the total after mixing. The formula is C1V1 + C2V2 = Cf(V1 + V2), where C is concentration and V is volume. For dilution problems (adding pure solvent), the second concentration is 0. Common scenarios include mixing solutions in chemistry, blending coffee beans of different prices, or combining investments at different interest rates. The key trick is setting up a table with Amount, Concentration, and Pure Substance columns for each component.
How do I decide which quantity to treat as the unknown?
Read the question sentence, not the data sentence. Whatever the problem asks for is the unknown, and every template here is one relation rearranged around it. Distance equals rate times time becomes time equals distance over rate, or rate equals distance over time, depending on which of the three is missing: 382.5 miles at 85 mph gives 4.5 hours. Selecting the unknown position tells the solver which rearrangement to apply, so the underlying relation never changes, only the algebra used to isolate a variable.
How does checking units catch a wrong setup before the arithmetic?
Dimensional analysis treats units as algebraic factors that must cancel to leave the units of the answer. Miles per hour multiplied by hours cancels the hours and leaves miles, which confirms the setup. Multiplying 60 mph by 45 minutes leaves mile-minutes per hour, a meaningless quantity, and signals that the 45 must first be converted to 0.75 hours to give 45 miles. The same test flags a percentage used as 8 when the relation expects the decimal 0.08.
What is alligation and when is it faster than the C1V1 equation?
Alligation is the merchants' shortcut for blending two known strengths to hit a target. Take the differences across the target: parts of the weaker solution are proportional to (stronger minus target), and parts of the stronger to (target minus weaker). To reach 20 percent from 10 percent and 50 percent stock, the ratio is (50-20) to (20-10), or 3 to 1, and three parts weak plus one part strong gives (0.3 + 0.5) / 4 = 0.20. Use it when volumes are unknown but the mixing ratio is what you need.
How do I handle a work problem where the second worker starts late?
Track work completed rather than elapsed time. If pipe A fills a pool in 6 hours it contributes 1/6 per hour, and running alone for one hour banks 1/6 of the job. The remaining 5/6 is then shared at the combined rate 1/6 + 1/4 = 5/12 per hour, taking (5/6) / (5/12) = 2 hours, for 3 hours total. The same accounting handles a worker who leaves early: subtract the fraction they completed and finish the remainder at the reduced rate.
Why do successive percentage changes multiply instead of adding?
Each change is applied to whatever the value has become, not to the original, so the operations compose as multipliers. A $50 item at 20 percent off is 50 x 0.8 = $40, and 8 percent tax makes it 40 x 1.08 = $43.20. The combined factor is 0.8 x 1.08 = 0.864, so the net effect is 13.6 percent below the sticker price, not 12 percent. For the same reason a 20 percent rise does not undo a 20 percent fall: 100 becomes 80, then 96.
References
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Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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