Question

Lisa drove 240 miles, then increased her speed by 20 miles per hour for 540 miles. If the second part of the drive took 3 hours longer than the first part, find her average speed.

Answer 1

Let u be speed while Lisa drove 240 miles and t be the time in completing 240 miles.

We have been given that Lisa increased her speed 20 mph than initial speed over next 540 miles. So her speed on next 540 miles will be $u+20$ mph.

Further more we are given that she took 3 hours more to complete the next 540 miles of the trip than she took in completing initial 240 miles. So she took $(t+3)$ hours in completing next 540 miles.

Since we know $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Now we will substitute our given values in our equation and find out the unknowns. After substitution we will get two equations and two unknowns.

$u=\frac{240}{t}.........(1)\\ \\ (u+20)=\frac{540}{t+3}........(2)$

Now we will substitute equation 1 in equation 2

$(\frac{240}{t}+20)=\frac{540}{t+3}$

Upon solving this equation, we get

$t=6$

Therefore, total time for Lisa to complete the entire trip is 6+6+3 = 15 hours.

And we know that total distance covered is 240+540 = 780 miles

Hence, average speed

$=\frac{\text{Total Distance}}{\text{Total Time}} = \frac{780}{15} = 52 \text{ miles per hour}$