## Distance, Time and Speed Word Problems | GMAT GRE Maths | MBA Crystal Ball

Since these distances add up to 45, I will add the distance expressions and set equal to the given total: 45 = 14t + 16t. Solve for t. A boat travels for three hours with a current of 3 mph and then returns the same distance against the current in four hours. What is the boat's speed in calm water? Distance covered by first train+Distance covered by second train = miles. 70t+20(t-2) = Solving this gives t = 4. So the two trains meet after 4 hours. Example 2. A train leaves from a station and moves at a certain speed. After 2 hours, another train leaves from the same station and moves in the same direction at a speed of 60 vjesnikws.ga: MBA Crystal Ball. Jul 12,  · When you are solving problems for distance, rate, and time, you will find it helpful to use diagrams or charts to organize the information and help you solve the problem. You will also apply the formula that solves distance, rate, and time, which is distance = rate x time. It is abbreviated as.

## "Distance" Word Problems: More Examples

Distance word problems are a common type of algebra word problems. They involve a scenario in which you need to figure out how fasthow faror how long one or more objects have traveled.

These are often called train problems because one of the most famous types of distance problems involves finding out when two trains heading toward each other cross paths.

In this lesson, you'll learn how to solve train problems and a few other common types of distance problems. But first, let's look at some basic principles that apply to any distance problem. There are three basic aspects to movement and travel: distancerateand time. To understand the difference among these, think about the last time you drove somewhere.

The distance is how far you traveled. The rate is how fast you traveled, distance problem solving. The time is how long the trip took. In other words, the distance you drove is equal to the rate at which you drove distance problem solving the amount of time you drove. For an example of how this would work in real life, just imagine your last trip was like this:. According to the formula, if distance problem solving multiply the rate and timethe product should be our distance.

And it is! We drove 50 mph for 0. What if we drove 60 mph instead of 50? How far could we drive in 30 minutes? We could use the same formula to figure this out. When you solve any distance problem, you'll have to do what we just did—use the formula to find distancerateor time.

Let's try another simple problem. On his day off, Lee took a trip to the zoo. He drove an average speed of 65 mph, and it took him two-and-a-half hours to get from his house to the zoo, distance problem solving. How far is the zoo from his house? First, we should identify the information we know. Remember, we're looking for any information about distance, rate, or time.

According to the problem:. This diagram is a start to understanding this problem, but we still distance problem solving to figure out what to do with the numbers for distancerateand time. To keep track of the information in the distance problem solving, we'll set up a table.

This might seem excessive now, but it's a good habit for even simple problems and can make solving complicated problems much easier. Here's what our table looks like:. The unknown distance is represented with the variable d.

To find dall we have to do is multiply 65 and 2. In other words, the distance Lee drove from his house to the zoo is Be careful to use the same units of measurement for rate and time. It's possible to multiply 65 miles per hour by 2.

However, what if the time had been written distance problem solving a different unit, like in minutes? In that case, you'd have to convert the time into hours so it would use the same unit as the rate. For example, distance problem solving, take a distance problem solving at this problem:. After work, Janae walked in her neighborhood for a half hour.

She walked a mile-and-a-half total. What was her average speed in miles per hour? The table is repeating the facts we already know from the problem. Janae walked one-and-a-half miles or 1. As always, we start distance problem solving our formula. Next, we'll fill in the formula with the information from our table. The distance problem solving is represented by r because we don't yet know how fast Janae was walking.

Since we're solving for rwe'll have to get it alone on one side of the equation. Our equation calls for r to be multiplied by 0. Janae walked 3 miles per hour. In the problems on this page, we solved for distance and rate of travel, distance problem solving, but you can also use the travel equation to solve for time. You can even use it to solve distance problem solving problems where you're trying to figure out the distance, rate, or time of two or more moving objects.

We'll look at problems like this on the next few pages. Bill took a trip to see a friend. His friend lives miles away. He drove in town at an average of 30 mph, then he drove on the interstate at an average of 70 mph. The trip took three-and-a-half hours total. How far did Bill drive on the interstate?

This problem is a classic two-part trip problem because it's asking you to find information about one part of a two-part trip. This problem might seem complicated, but don't be intimidated! Let's start with the table. Take another look at the problem.

This time, the information relating to distancerateand time has been underlined. He drove in town at an distance problem solving of 30 mphthen he drove on the interstate at an average of 70 mph. If you tried to fill in the table the way we did on the last page, distance problem solving, you might have noticed a problem: There's too much information. Distance problem solving instance, the problem contains two rates— 30 mph and 70 mph, distance problem solving.

To include all of this information, let's create a table with an extra row. The top row of numbers and variables will be labeled in townand the bottom row will be labeled interstate, distance problem solving.

We filled in the rates, but what about the distance and time? If you look back at the problem, you'll see that these are the total figures, meaning they include both the time in town and on the interstate. So the total distance distance problem solving This means this is true:. Together, the interstate distance and in-town distance are equal to the total distance. In any case, we're trying to find out how far Bill drove on the interstateso let's represent this number with d.

If the interstate distance is dit means the in-town distance is a number that equals the total, distance problem solving,when added to d. In other words, it's equal to - d. We can use the same technique to fill in the time column. The total time is 3. If we say the time on the interstate is tthen the remaining time in town is equal to 3. We can fill in the rest of our chart. Now we can work on solving the problem. The main difference between the problems on the first page and this problem is that this problem distance problem solving two equations.

Here's the one for in-town travel :. If you tried to solve either of these on its own, you might have found it impossible: since each equation contains two unknown variables, they can't be solved on their own.

Try for yourself. If you work either equation on its own, distance problem solving, you won't be able to find a numerical value for d.

In order to find the value of dwe'll also have to know the value of t. We can find the value of t in both problems by combining them. Let's take another look at our travel equation for interstate travel. While we don't know the numerical value of dthis equation does tell us that d distance problem solving equal to 70 t. Since 70 t and d are equalwe can replace d with 70 t. Substituting 70 t for d in our equation for interstate travel won't help us find the value of t —all it tells us is that 70 t is equal to itself, which we already knew.

When we replace the d in that equation with 70 tdistance problem solving, the equation suddenly gets much easier to solve. Our new equation might look more complicated, but it's actually something we can solve. This is because it only has one variable: t. Once we find twe can use it to calculate the value of d —and find the answer to our problem. To simplify this equation and find the value of twe'll have to get the t alone on one side of the equals sign.

We'll also have to simplify the right side as much as possible. Let's start with the right side: 30 times 3. Next, let's cancel out the next to 70 t.

### Algebra Topics: Distance Word Problems

Since these distances add up to 45, I will add the distance expressions and set equal to the given total: 45 = 14t + 16t. Solve for t. A boat travels for three hours with a current of 3 mph and then returns the same distance against the current in four hours. What is the boat's speed in calm water? Why is the distance just "d" for both trains? Partly, that's because the problem doesn't say how far the trains actually went. But mostly it's because they went the same distance as far as I'm concerned, because I'm only counting from the depot to wherever they met. Solution to Problem 7: Let x be John's rate in traveling between the two cities. The rate of Peter will be x + We use the rate-time-distance formula to write the distance D traveled by John and Peter (same distance D) D = 3 x and D = 2(x + 20) The first equation can be solved for x to give x = D / 3 Substitute x by D / 3 into the second.