Video: Solving Word Problems Involving Constant Rate

The given table shows the total distance traveled by a bus driving at a constant speed. Using this information, determine how far the bus will have traveled after 10 hours.

03:31

Video Transcript

The given table shows the distance traveled by a bus driving at a constant speed. Using this information, determine how far the bus will travel after 10 hours.

So here in this row, we have the time in hours. And then in this row, we have the distance in miles. So we read the table by looking at the columns. So, for this first column, it’s saying that the bus traveled 142 miles in two hours. This column will tell us that the bus traveled 404.7 miles in 5.7 hours. And we will follow the same pattern for the last two columns.

So we’ve been asked to determine how far the bus will travel after 10 hours. So, after 10 hours, how many miles did the bus travel? We are also told that the bus travels at a constant speed. So notice, this question has speed, time, and distance. And they’re all through related. Speed is equal to the distance divided by the time. And we are told that the bus traveled at a constant speed. But it didn’t tell us what the constant speed was. So we can find that out, because the distance is found in this bottom row and the time is found in the top row. So we can use one of these sets to find the speed that has been constant throughout this entire time.

Let’s use this column. So the speed will be equal to the distance, 142 miles, divided by the time, two hours. And 142 divided by two is equal to 71. So the speed will be 71 miles per hour. Now, while we are told that the speed is constant, we can always double-check that during a different time frame that the speed did stay the same, 71 miles per hour.

Let’s check the speed using this column. So we take 404.7 miles and divide it by 5.7 hours. And, just as we should, we got 71 miles per hour. And being extra careful we could check here. And we get 71 miles per hour. And lastly here, getting 71 miles per hour. So the speed did indeed stay constant this entire time. So we know that our constant speed was 71 miles per hour.

We are asked to determine how far the bus will travel after 10 hours. So we’re given a time. And we’re asked to determine a distance. So let’s rearrange our equation, so we have distance is equal to something. If we multiply both sides of the equation by time, we would have solved for distance. So we have that distance is equal to speed times time. So we can now plug into our equation and solve for the distance that the bus would have traveled after 10 hours.

So 10 hours will be our time. And we’ve found the constant speed of the bus was 71 miles per hour, so we find the distance by taking 71 times 10, which would be 710. And this is the distance, so what would be in terms of miles. If we would be curious about how the units work out and how we get miles for distance, while the speed was 71 miles per hour and the time was 10 hours. Now 71 miles per hour can be rewritten as 71 miles per hour. So when we multiply the 71 and 10, we get 710. The hours cancel and we’re left with miles. Therefore, after 10 hours the bus will travel 710 miles.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.