Problem Solving

A car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?

A. 6
B. 8
C. 11
D. 12
E. 14

[spoiler]OA=A[/spoiler].

Why is A the correct answer? I need some help here. Please. Thanks in advance.

Hello Gmat_mission.

Let's take a look at your question

A car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?

We have the following $$Average\ Speed=\frac{\text{distance}\ first\ part+\ \text{distance}\ \text{second}\ part}{time\ first\ part+time\ \text{second}\ part}.$$ So, we have $$60=\frac{55\cdot4+70\cdot t_2}{4+t_2}$$ $$240+60t_2=220+70\cdot t_2$$ $$70t_2-60t_2=240-220$$ $$10t_2=20$$ $$t_2=2.$$ Therefore, the entire trip last 4+2 hours, that is to say, 6 hours.

This implies that the correct answer is the option A.

I hope this explanation helps you.

Regards.

Gmat_mission wrote:A car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?

A. 6
B. 8
C. 11
D. 12
E. 14

Since the car travels at 55 mph for 4 hours, the distance traveled in the first 4 hours = rt = 55*4 = 220 miles.
We can PLUG IN THE ANSWERS, which represent the total time.
When the correct answer is plugged in, the average speed for the whole trip = 60 mph.

B: 8 hours, implying that the last 4 hours are traveled at 70 mph
Since the car travels at 70 mph for 4 hours, the distance traveled in the last 4 hours = rt = 70*4 = 280 miles.
Average speed for the entire trip = (total distance)/(total time) = (220+280)/8 = 500/8 = 61.25 mph.

The average speed for the entire trip is too high.
For the average speed to decrease, the total time must also decrease, so that less time is spent at the higher speed (70 mph).

The correct answer is A.

A: 6 hours, implying that the last 2 hours are traveled at 70 mph
Since the car travels at 70 mph for 2 hours, the distance traveled in the last 2 hours = rt = 70*2 = 140 miles.
Average speed for the entire trip = (total distance)/(total time) = (220+140)/6 = 360/6 = 60 mph.
Success!