If you drive at 60mph for 1 hour, then 70mph for another hour, what was your average speed?

To find the average speed, we need to consider the total distance traveled and the total time it took to cover that distance. It’s important to note that average speed is not simply the arithmetic mean of the two speeds (i.e., not (60 + 70)/2 ).

Let’s break down the problem:

In the first hour, you travel at 60 mph. So, you cover 60 miles in that hour:

Distance₁ = Speed₁ × Time₁ = 60miles/hour × 1hour = 60miles

In the second hour, you travel at 70 mph. Thus, you cover 70 miles in that hour:

Distance₂ = Speed₂ × Time₂ = 70miles/hour × 1hour = 70miles

Now let’s find the total distance traveled:

$$\begin{aligned} \text{Total Distance} &= \text{Distance}_1 + \text{Distance}_2 \\ &= 60 \text{miles} + 70 \text{miles} \\ &= 130 \text{miles}\end{aligned}$$

The total time spent is 2 hours (1 hour at 60 mph and 1 hour at 70 mph).

Now we can find the average speed, which is the total distance divided by the total time:

$$\begin{aligned} \text{Average Speed} &= \frac{\text{Total Distance}}{\text{Total Time}} \\ &= \frac{130 \text{miles}}{2 \text{hours}} \\ &= 65 \text{miles/hour}\end{aligned}$$

So, the average speed during this 2-hour trip is 65 mph.