Question

Elizabeth drove the first half of the trip at 36 mi/h. At what speed should she cover the remaining half of the trip in order to average 45 mi/h for the entire trip?

Answer 1

Let the total distance of the trip be d. And let x be the required speed on the second half of the trip.
Time for first half of trip = d/(2 x 36) hours.
Time for second half of trip = d/2x.
The total time for the trip is then:
$\frac{d}{72}+\frac{d}{2x}=\frac{d(x+36)[tex]\frac{d}{45}=\frac{d(x+36)}{72x}$}{72x}[/tex]
However the total time for the trip must also be d/45.
Therefore we can write and solve the following equation:
$\frac{d}{45}=\frac{d(x+36)}{72x}$
Dividing both sides by d, and then cross-multiplying gives:
$72x=45x+(36\times45)$
27x = 1620
x = 60
The answer is 60 mi/h.