Video: Calculating the Distance Traveled by an Object given Its Speed

An airplane travels at a speed of 800 km/h for 3.5 hours. How many kilometers does the airplane travel?

02:51

Video Transcript

An airplane travels at a speed of 800 kilometers per hour for 3.5 hours. How many kilometers does the airplane travel?

In this question, we have an airplane that we’re told travels at a speed of 800 kilometers per hour. We’ll label the speed of the airplane as 𝑠. So we can write that 𝑠 is equal to 800 kilometers per hour. We’re told that this airplane travels for a time of 3.5 hours. So if we label this time 𝑑, then we can say that 𝑑 is equal to 3.5 hours. The question asks us, how many kilometers does the airplane travel? So we want to find the distance that the plane covers in units of kilometers. We’ll label this distance as 𝑑, and this is the quantity that we’re trying to find.

So we know the speed that the airplane travels and the length of time that it travels for. And what we’re trying to find is the distance that it covers in that time. We can recall that there is a formula that relates the three quantities speed, distance, and time. Specifically, for a speed labeled 𝑠, a distance 𝑑, and a time 𝑑, we have that 𝑠 is equal to 𝑑 divided by 𝑑. In this case, we know the value of 𝑠 and we know the value of 𝑑. It’s 𝑑 that we’re trying to find. So let’s rearrange this formula in order to make 𝑑 the subject.

If we multiply both sides by 𝑑, then on the right-hand side, the 𝑑’s in the numerator and denominator cancel each other out. Then, swapping the left- and right-hand sides of the equation over, we have that distance 𝑑 is equal to speed 𝑠 multiplied by time 𝑑. Now we just need to take our values of 𝑠 and 𝑑 and substitute them into this equation to calculate 𝑑. Since our speed is given in units of kilometers per hour and our time is given in units of hours, then the distance that we calculate will have units of kilometers, which is what the question asked us for.

Substituting in these values, we have that 𝑑 is equal to our speed of 800 kilometers per hour multiplied by our time of 3.5 hours. When we do this multiplication, we find a result of 2,800 kilometers. And so our answer to the question β€œHow many kilometers does the airplane travel?” is 2,800 kilometers.

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