Enter any two variables to solve for the third using the formula d = r × t.
Distance (d)
Average Rate/Speed (r)
Time (t)
Result:
Understanding the Distance, Rate, and Time Formula
The relationship between distance, rate (speed), and time is a fundamental concept in physics and basic mathematics. The core formula used to solve these problems is:
d = r × t
Distance (d): The total length of the path traveled.
Rate (r): The speed at which an object travels (distance per unit of time).
Time (t): The duration for which the object is moving.
How to Solve for Each Variable
Depending on which piece of information you are missing, you can rearrange the formula:
To find Distance: Multiply Rate by Time (d = r × t).
To find Rate: Divide Distance by Time (r = d / t).
To find Time: Divide Distance by Rate (t = d / r).
Example 1: Solving for Distance
If a car travels at a constant speed of 65 mph for 4 hours, how far does it go? Calculation: 65 (Rate) × 4 (Time) = 260 miles.
Example 2: Solving for Rate
If a runner completes a 10-mile race in 2 hours, what was their average speed? Calculation: 10 (Distance) / 2 (Time) = 5 miles per hour.
Example 3: Solving for Time
A plane needs to fly 1,500 miles. If it flies at 500 mph, how long will the trip take? Calculation: 1,500 (Distance) / 500 (Rate) = 3 hours.
Important Tips for Accuracy
When solving distance-rate-time problems, always ensure that your units are consistent. For example, if your rate is in miles per hour (mph), your time must be in hours and your distance must be in miles. If you have time in minutes, divide by 60 to convert it to hours before using it in the formula.
function updateFields() {
var mode = document.getElementById("solveFor").value;
document.getElementById("distanceFields").style.display = (mode === "distance") ? "block" : "none";
document.getElementById("rateFields").style.display = (mode === "rate") ? "block" : "none";
document.getElementById("timeFields").style.display = (mode === "time") ? "block" : "none";
document.getElementById("drtResult").style.display = "none";
}
function calculateDRT() {
var mode = document.getElementById("solveFor").value;
var resultText = document.getElementById("resultText");
var formulaText = document.getElementById("formulaText");
var resultDiv = document.getElementById("drtResult");
var output = "";
var formula = "";
if (mode === "distance") {
var r = parseFloat(document.getElementById("dist_rate").value);
var t = parseFloat(document.getElementById("dist_time").value);
if (isNaN(r) || isNaN(t) || r < 0 || t < 0) {
alert("Please enter valid positive numbers for Rate and Time.");
return;
}
var d = r * t;
output = "The total Distance is " + d.toLocaleString(undefined, {maximumFractionDigits: 4}) + " units.";
formula = "Calculation: " + r + " (Rate) × " + t + " (Time) = " + d.toLocaleString();
} else if (mode === "rate") {
var d = parseFloat(document.getElementById("rate_dist").value);
var t = parseFloat(document.getElementById("rate_time").value);
if (isNaN(d) || isNaN(t) || d < 0 || t <= 0) {
alert("Please enter valid positive numbers. Time must be greater than zero.");
return;
}
var r = d / t;
output = "The average Rate (Speed) is " + r.toLocaleString(undefined, {maximumFractionDigits: 4}) + " units per hour.";
formula = "Calculation: " + d + " (Distance) / " + t + " (Time) = " + r.toLocaleString();
} else if (mode === "time") {
var d = parseFloat(document.getElementById("time_dist").value);
var r = parseFloat(document.getElementById("time_rate").value);
if (isNaN(d) || isNaN(r) || d < 0 || r <= 0) {
alert("Please enter valid positive numbers. Rate must be greater than zero.");
return;
}
var t = d / r;
output = "The total Time required is " + t.toLocaleString(undefined, {maximumFractionDigits: 4}) + " hours.";
formula = "Calculation: " + d + " (Distance) / " + r + " (Rate) = " + t.toLocaleString();
}
resultText.innerHTML = output;
formulaText.innerHTML = formula;
resultDiv.style.display = "block";
}
// Initialize the default view
updateFields();