Pick the problem type, enter the numbers, and the tool writes the equation and solves it. A parent aged 40 and a child aged 10 are in a 2 to 1 age ratio in 20 years. Two workers who take 6 and 3 hours alone finish together in 2 hours. Two cars at 60 and 80 per hour, 420 apart, meet in 3 hours.
Every number is an exact fraction, and each answer shows the equation it came from, so you can check the set-up as well as the result. Anything outside these four types is left alone rather than guessed.
Enter the numbers from your problem. The equation and answer update as you type.
In how many years will the older person be a whole multiple of the younger one’s age?
e.g. 2 for “twice as old”
Answer
In 20 years the older person will be 2 times as old as the younger one.
How the equation is built
Equation:
40 + x = 2(10 + x)
Solving it, step by step (x = 20)
One of each type, with the equation written out.
A parent is 40 and a child is 10. In how many years will the parent be twice as old as the child?
x = 20 years. Check: the parent is 60 and the child is 30.
You have 10 litres of 20% solution. How much 50% solution must you add to get 30%?
x = 5 litres. Check: 20% of 10 + 50% of 5 = 4.5 and 30% of 15 = 4.5.
Two cars start 420 km apart at 60 and 80 km/h, driving toward each other. When do they meet? Then: if the 60 km/h car left 2 hours earlier, when does the 80 km/h car catch it?
They meet after 3 hours; the chase ends 6 hours after the faster car starts (480 km from the start).
Person A paints a room in 6 hours, person B in 3 hours. How long together?
x = 2 hours. Check: 2/6 + 2/3 = 1/3 + 2/3 = 1.
Every equation here can be pasted into the Math Problem Solver. For the underlying methods see the linear equations guide and systems of equations for problems with two unknowns.
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Read it twice, decide what is being asked and call that x, write what each quantity is in terms of x, find the sentence that says two quantities are equal, and turn it into an equation. Solve the equation, then put the answer back into the story to check that it makes sense.
Let x be the number of years from now, add x to both ages, and write the relationship as an equation. A parent aged 40 and a child aged 10: the parent is twice as old when 40 + x = 2(10 + x), which gives x = 20. In 20 years they are 60 and 30. A negative x means it already happened that many years ago.
Track the pure substance. Amount before + amount added = amount after. Adding x litres of 50% solution to 10 litres of 20% solution to reach 30%: 20(10) + 50x = 30(10 + x), so 20x = 100 and x = 5 litres. The target strength must sit between the two strengths you are mixing.
Distance = rate × time. For two travellers moving toward each other, their speeds add: at 60 and 80 per hour, a 420 gap closes in 420 ÷ 140 = 3 hours. For a chase, both travellers cover the same distance at the catch-up point: 60(x + 2) = 80x gives x = 6 hours after the faster one starts.
Add the fractions of the job each person does in x hours. If A takes 6 hours alone and B takes 3, then x/6 + x/3 = 1, so (1/2)x = 1 and x = 2 hours together. A third person is just one more x/h term.
It covers these four types with a single unknown. Problems with several unknowns, percentages of percentages, geometry or calculus are not guessed at: the Math Problem Solver handles equations and systems you write yourself, and the MathAI GPT solver can take the whole question typed or as a photo.