Solve linear motion problems easily using the d = rt formula.
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var labelB = document.getElementById("labelB");
var inputA = document.getElementById("inputA");
var inputB = document.getElementById("inputB");
// Reset inputs
inputA.value = "";
inputB.value = "";
document.getElementById("resultBox").style.display = "none";
if (type === "distance") {
labelA.innerText = "Rate (Speed):";
inputA.placeholder = "e.g. 60 (miles/hour)";
labelB.innerText = "Time:";
inputB.placeholder = "e.g. 2 (hours)";
} else if (type === "rate") {
labelA.innerText = "Distance:";
inputA.placeholder = "e.g. 120 (miles)";
labelB.innerText = "Time:";
inputB.placeholder = "e.g. 2 (hours)";
} else if (type === "time") {
labelA.innerText = "Distance:";
inputA.placeholder = "e.g. 120 (miles)";
labelB.innerText = "Rate (Speed):";
inputB.placeholder = "e.g. 60 (miles/hour)";
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function calculateDRT() {
var type = document.getElementById("solveType").value;
var valA = parseFloat(document.getElementById("inputA").value);
var valB = parseFloat(document.getElementById("inputB").value);
var resultBox = document.getElementById("resultBox");
var mainResult = document.getElementById("mainResult");
var steps = document.getElementById("calculationSteps");
if (isNaN(valA) || isNaN(valB)) {
alert("Please enter valid numbers for both fields.");
return;
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if (valA < 0 || valB < 0) {
alert("Distance, Rate, and Time values generally shouldn't be negative in this context.");
return;
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var result = 0;
var formulaHTML = "";
var stepHTML = "";
var unit = "";
if (type === "distance") {
// d = r * t
result = valA * valB;
formulaHTML = "d = r × t";
stepHTML = "Multiply Rate (" + valA + ") by Time (" + valB + ").";
unit = "Distance Units";
mainResult.innerHTML = "Distance = " + result.toFixed(2);
} else if (type === "rate") {
// r = d / t
if (valB === 0) {
alert("Time cannot be zero.");
return;
}
result = valA / valB;
formulaHTML = "r = d / t";
stepHTML = "Divide Distance (" + valA + ") by Time (" + valB + ").";
unit = "Speed Units";
mainResult.innerHTML = "Rate = " + result.toFixed(2);
} else if (type === "time") {
// t = d / r
if (valB === 0) {
alert("Rate cannot be zero.");
return;
}
result = valA / valB;
formulaHTML = "t = d / r";
stepHTML = "Divide Distance (" + valA + ") by Rate (" + valB + ").";
unit = "Time Units";
mainResult.innerHTML = "Time = " + result.toFixed(2);
}
steps.innerHTML =
"
" +
"1. Identify the formula:
" +
"2. Substitute values: " + stepHTML + "" +
"3. Result:
(in consistent " + unit + ").";
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Understanding the Distance Rate Time Formula
The relationship between distance, rate (speed), and time is one of the most fundamental concepts in algebra and physics. It represents a linear equation of motion, assuming a constant speed. Whether you are calculating how long a road trip will take, the speed of a runner, or the distance a plane travels, this calculator helps you solve for the unknown variable.
The core formula is represented algebraically as:
d = r × t
Where:
- d = Distance (how far you travel)
- r = Rate (speed or velocity)
- t = Time (duration of travel)
Variations of the Equation
Depending on which variable you are trying to find, the linear equation can be rearranged into three forms. This calculator automatically switches between these forms based on your selection:
1. Solving for Distance
If you know your speed and how long you have been traveling, you multiply them to find the distance.
Equation: d = r × t
Example: If you drive at 60 mph for 2 hours, calculation is 60 × 2 = 120 miles.
2. Solving for Rate (Speed)
If you know the total distance traveled and the total time taken, you divide distance by time to find the average speed.
Equation: r = d / t
Example: If you ran 10 kilometers in 1 hour, calculation is 10 / 1 = 10 km/h.
3. Solving for Time
If you know the distance you need to cover and the speed at which you are moving, divide the distance by the rate to find out how long it will take.
Equation: t = d / r
Example: If you need to travel 300 miles and your train moves at 100 mph, calculation is 300 / 100 = 3 hours.
Importance of Consistent Units
When using the Distance Rate Time Linear Equation Calculator, it is critical to ensure your units match. The variables must be consistent for the math to work correctly.
- If Rate is in Miles per Hour (mph), Time must be in Hours, and Distance will be in Miles.
- If Rate is in Meters per Second (m/s), Time must be in Seconds, and Distance will be in Meters.
If you input time in minutes but your speed is in miles per hour, you must convert the minutes to hours (e.g., 30 minutes = 0.5 hours) before entering the value into the calculator.
Linear Equations in Real Life
Graphically, uniform motion is a straight line, hence the term "linear equation." If you were to graph Distance (y-axis) vs. Time (x-axis), the slope of the line represents the Rate (Speed). A steeper line indicates a faster speed, while a flatter line indicates a slower speed. This calculator solves that linear relationship instantly for any two known variables.