Question

In the race Math $600$, drivers must complete $200$ laps of $3$ miles each. Dave drove the first $150$ laps at $180$ mph and the last $50$ laps at $200$ mph. What was Dave's average speed for the race, in miles per hour? Express your answer as a common fraction.

Answer 1

Answer:

$\text{Average speed}\approx 184.62\frac{\text{ miles}}{\text{ hours}}$

Step-by-step explanation:

We have been given that in the race Math 600, drivers must complete 200 laps of 3 miles each. Dave drove the first 150 laps at 180 mph and the last 50 laps at 200 mph.

First of all, we will find the number of miles in 150 laps and 50 laps as:

$150\times 3\text{ Miles}=450\text{ Miles}$

$50\times 3\text{ Miles}=150\text{ Miles}$

Now, we will find time taken to complete each distance as:

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

$\text{Time}=\frac{\text{ 450 Miles}}{\frac{\text{180 Miles}}{\text{Hour}}}$

$\text{Time}=\frac{\text{ 450 Miles}}{\text{180 Miles}}\times \text{Hour}}$

$\text{Time}=2.5 \text{ Hour}$

$\text{Time}=\frac{\text{ 150 Miles}}{\frac{\text{200 Miles}}{\text{Hour}}}$

$\text{Time}=\frac{\text{ 150 Miles}}{\text{200 Miles}}\times\text{ Hour}$

$\text{Time}=0.75\text{ Hour}$

To find average speed, we will divide total distance traveled by total time as:

$\text{Average speed}=\frac{\text{450 miles +150 miles}}{\text{2.5 hours + 0.75 hours}}$

$\text{Average speed}=\frac{\text{600 miles}}{\text{3.25 hours}}$

$\text{Average speed}=184.615\frac{\text{ miles}}{\text{ hours}}$

$\text{Average speed}\approx 184.62\frac{\text{ miles}}{\text{ hours}}$

Therefore, the average speed in approximately 184.62 miles per hour.