For the first 5 hours of a trip, a plane averaged

Gmat_mission wrote:For the first 5 hours of a trip, a plane averaged 120 kilometers per hour. For the remainder of the trip, the plane traveled an average speed of 180 kilometers per hour. If the average speed for the entire trip was 170 kilometers per hour, how many hours long was the entire trip?

A. 15
B. 20
C. 25
D. 30
E. 35

[spoiler]OA=D[/spoiler].

What is the formula that I should use here? I got confused here.

Hi.

This is how I'd solve it.

We have that $$average\ speed\ =\ \frac{\text{Total}\ \text{ Distance}}{\text{Total}\ \text{Time}}.$$ Now, "For the first 5 hours of a trip, a plane averaged 120 kilometers per hour" implies that the first part of the trip are $$d_1=v_1\cdot t_1\ =\ 120\cdot5=600\ km.$$ Now, the second one is $$d_2=v_2\cdot t_2\ =\ 180\cdot t_2.$$ Now, replacing this on the first equation we have that: $$Average\ Speed\ =\ \frac{\text{Total}\ \text{ Distance}}{\text{Total}\ \ \ \text{Time}}$$ $$170=\ \frac{d_1+d_2}{t_1+t_2}=\frac{600+d_2}{5+t_2}=\frac{600+180t_2}{5+t_2}$$ $$850+170t_2=600+180t_2$$ $$850-600=180t_2-170t_2$$ $$250=10t_2$$ $$t_2=25.$$ Now, the entire trip was $$T=t_1+t_2=5+25=30\ hours\ long.$$ Therefore, the correct answer is the option D.

I hope it helps you.