Solve each problem. How long will it take a car to travel 400 mi ...

Question

Solve each problem. How long will it take a car to travel 400 mi at an average rate of 50 mph?

Accepted Answer

Welcome back. I am so glad you're here. We are asked to calculate the length of time. So we're trying to find the time that it takes a rabbit to cover a total distance of six miles. We have a distance of six miles. If it was hopping along a straight routed, an average rate of 30 MPH. That is a fast hop. Alright, so we've got a rate Equals 30 mph. I'm going to write that as miles over hours, MPH. Oh my gosh, this bunny is fast anyway, to find the time we recall from previous lessons that when we're dealing with distance rate and time, we have the distance formula formula, which is distance equals rate, times time. And now let's plug in what we know. We know the distance, the distance is six miles. We know the rate, the rate is 30 mph And we don't know the time. That's what we're trying to find. In order to get that time by itself, we need to divide both sides by the 30 mph, Dividing six x 30 mph. And now on the left hand, side. Let's rewrite that a little bit. We've got six miles divided by 30 miles over hours and we know that when we're taking two fractions and dividing them, that's the same as taking the first one times the reciprocal of the second one. So that would be one hour over 30 miles. And here are miles units cancel out and we can multiply straight across. We have six times one that's six and it's hours over 30 and we can simplify 6/30 6/30 equals 1/5 of an hour. So amazingly enough, this rabbit covered a distance of six miles in 1/5 of an hour. That is impressive. And Uh we have our answer except all of our answers here are in minutes. So we need to do some more unit conversion. We need to take 1/5 of an hour and convert that to minutes in order to do that, we need our units to cancel out. So we're going to multiply this by a fraction. We want our hours on the bottom so that hours cancel out and then minutes on the top So that we will have minutes in our answer. And how many minutes are there in an hour? There are 60 minutes in one hour. Now, we can cancel out. Our, our units are minute. Units are good and we multiply straight across the enumerators. One time 60 is 60 multiply across the denominators. Five times one is five So we have 60/5 minutes while divided by five is 12. So this is in 12 minutes. That rabbit covered a distance of six miles at MPH. Wow. Alright, looking at our answer choices, this matches with answer choice. B well done. We'll catch you on the next one.

Solve each problem. How long will it take a car to travel 400 mi at an average rate of 50 mph?

Key Concepts

Distance, Rate, and Time Relationship

Unit Consistency

Algebraic Manipulation

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