# John drove for two hours at the speed of 50 miles per hour (mph) and another x hours at the speed of 55 mph. If the average speed of the entire journey is 53 mph, which of the following could be used to find x?

The idea here is that you need to work backwards from the definition of the average speed to determine how much time did John spend driving at 55 mph.

The average speed can be thought of as being the ratio between the total distance travelled and the total time needed to travel it.

At the same time, distance can be expressed as the product between velocity (in this case, speed) and time.

So, if John drove for 2 hours at 50 mph, then he covered a distance of

The second part of the total distance was travelled at 55 mph for x hours, so you can say that

The total distance travelled is equal to

The total time needed was

This means that the average speed is

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To find the value of x, you can use the formula for average speed:

Average speed = Total distance / Total time

In this case, the total time is the sum of the time John drove at 50 mph and the time he drove at 55 mph.

Let's denote the time John drove at 50 mph as 2 hours (since he drove for two hours at that speed).

So, the total time is 2 hours + x hours.

The total distance traveled is the sum of the distances traveled at each speed. Distance = Speed × Time.

Distance traveled at 50 mph = 50 mph × 2 hours = 100 miles

Distance traveled at 55 mph = 55 mph × x hours = 55x miles

Therefore, the total distance is 100 miles + 55x miles.

We know that the average speed for the entire journey is 53 mph.

So, we can set up the equation:

53 mph = (100 miles + 55x miles) / (2 hours + x hours)

To solve for x, you can cross multiply and solve the resulting equation. Once you have the value of x, you can use it to determine the correct option from the given choices.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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