Understand
Read the story twice. Name the unknown, list what is given, and spot the relationship — closing gap, equal positions, amounts that must total.
Word problems, solved the staged way
Word problems are translation problems. So we do not jump to the answer — we walk through understand → set up → solve → verify against the story, showing the translation happen. Try it live:
Two vehicles start apart and drive toward each other. When do they meet?
- ✓100% free — no paywall, ever
- ✓No sign-up, no app
- ✓Verified against the story, not just the equation
The four-stage method
Teachers call it “reading the problem”. We made it mechanical — four stages, in order, every time. Stage 4 is the one that makes VerifySolve different: the answer must satisfy the story itself.
Set up the equation
Translate the relationship into algebra with a d = rt chart or the two mixture equations. This stage is the actual skill; the rest is routine.
Solve
Plain algebra with exact fractions, every step shown. Nothing here should surprise you if Stage 2 was right.
Verify against the story
Plug the answer back into the STORY — not just the equation. Distances must sum to the gap, positions must coincide, totals must match. If the story disagrees, the setup was wrong.
A truck has a 30-mile head start at 40 mph; a car chases at 55 mph. When does the car catch up?
- 1.Stage 1 — Understand: the 30-mile gap closes at 55 − 40 = 15 mph
- 2.Stage 2 — Set up: positions equal when 55t = 40t + 30
- 3.Stage 3 — Solve: 15t = 30
t = 2 hours
Stage 4 — Verified against the story: after 2 hours the car is at mile 110, and the truck is at 30 + 40·2 = mile 110. Same place, same time ✓.
Word problem families
Live families have their own staged solver pages. Coming families are shown honestly as in development — we would rather label a gap than fill it with a generic calculator.
Live
Distance, Rate & Time
Meeting, catch-up and round-trip stories built on d = rt — the most-tested word problem family in algebra.
Open the staged solver →LiveMixture Problems
How much of each solution or ingredient to hit an exact target percent or price. Two equations, staged.
Open the staged solver →Coming soon
Percent Problems
Discounts, tax, interest and percent change stories.
Coming soon
Age Problems
“In five years, twice as old” — present and future ages as equations.
Coming soon
Work Problems
Two people or machines finishing one job together.
Coming soon
Coin & Money Problems
Counts and values of coins and bills as a two-equation system.
Word problems — questions
Why do word problems feel harder than plain equations?
Because the equation is hidden inside a story. The solving is usually easy — the hard part is translation: deciding what x represents, which quantities relate, and which formula connects them. That is why our solver works in stages and shows the translation happening, instead of jumping straight to algebra.
What is the staged method?
Four stages. Stage 1 — Understand: name the unknown and the relationships in the story. Stage 2 — Set up: write the equation(s) those relationships imply. Stage 3 — Solve: ordinary algebra, with steps. Stage 4 — Verify: test the answer against the story’s own conditions (distances must add up, amounts must total, positions must coincide). A solution that fails Stage 4 was a wrong setup, not a wrong calculation.
Which word problem types are covered right now?
Distance-rate-time problems (meeting, catch-up, round trip) and mixture problems (percent and price) have dedicated staged solvers. Percent, age, work-rate and coin problems are in development — the hub shows honestly which families are live and which are coming.
How is verification different here from a normal calculator?
A normal solver checks the answer against the equation you built. We check against the story you were given. If your equation was the wrong translation, a normal check passes anyway — ours catches it, because the story conditions are tested independently of the setup.
Can I solve word problems that need two unknowns?
Mixture problems already work that way under the hood (two equations, two unknowns — the solver shows both). For hand-built systems from other story types, our system of equations calculator handles the algebra once you have translated.
Is the word problem solver free?
Yes — free, no sign-up, no app, with the full staged solution and story verification included.
Keep solving
Equation Solver →
Once a story becomes an equation, solve it here with plug-back proof.
Algebra Calculator →
The underlying algebra toolkit — equations, systems, factoring.
SAT Math Practice →
Word problems are SAT staples — practise them in test format.
System of Equations Calculator →
Two-unknown stories end up here. Solve the system directly.
A note on honest use: VerifySolve is built for learning. Use the stages to understand how stories become equations, then close the tab and translate the next one yourself — that translation is the skill being tested. If your teacher or school has a policy on calculators, follow it.