A cyclist rides at an average speed of 18 mi per hour. If she wants to bike 212 km, how long (in hours) must she ride?

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Hey everyone. And welcome back to another video. A cyclist rides at an average speed of 18 MPH. If she wants to bike 212 kilometers, how long in hours must she ride? We are given for answer choices. A 0.91 B 8.5 C 7.3 and D 11 all given in units of hours. So let's use dimensional analysis, right? This is the easiest way to solve any sort of problem. When we want to convert units, we are given 212 kilometers. That's our starting quantity. So we can just include it. And now let's think about the conversion factors that we need to use. Well, our speed is given in MPH. The problem is that if our distance units are kilometers, we want to switch them into miles. And for that purpose, we need to include our first conversion factor. So let's go ahead and do that. We want to cancel out kilometers. So we put them on the bottom of the fraction and on top, we will put miles. Now the relationship between miles and kilometers is as false. We know that one mile is equivalent to one point 609 we kilometers. So what we have achieved here is a conversion which allows us to go from kilometers into miles, right? So we have our miles so far and now we want to get ours. So we're going to introduce another multiplication sign. And now what else do we have? Well, we have our speed. So first of all, we are going to include another conversion factor, we have miles to cancel out. So we are going to put miles into our denominator and we will put ours on top because this is our desired quantity. So in this case, we will be able to cancel out mile and the final quantity will be ours. Meaning meaning we are on the right track. So now if we have 18 MPH, we can just say that we put 18 into our denominator per hour means per one hour. So that'll be one on top. And now eventually we just get our answer. We are multiplying 212 by one by another one and then dividing by 1.6093 and 18, which gives us 7.3 hours. This essentially corresponds to the answer choice. C 7.3 hours is the required time. Thank you for watching.

A cyclist rides at an average speed of 18 mi per hour. If she wants to bike 212 km, how long (in hours) must she ride?

Verified Solution

Key Concepts

Unit Conversion

Speed, Distance, and Time Relationship

Average Speed