Hey Vincen,

We need to consider each segment of the trip separately.

We know that distance = rate * time. Rearranged, this gives us time = distance / rate. So for each segment of the trip, we should be able to divide the distance by the rate (speed) to give the time. Then, we can add together the time for the three segments to give the total time of the trip.

Segment 1: 5D / 2v
Segment 2: 4D / 3v
Segment 3: D / 6v

Adding the three together gives:
$$\frac{5D}{2v}+\frac{4D}{3v}+\frac{D}{6v}$$
Finally, we find a common denominator (6v) and simplify:
$$\frac{5D\left(3\right)}{2v\left(3\right)}+\frac{4D\left(2\right)}{3v\left(2\right)}+\frac{D}{6v}$$ $$\frac{15D}{6v}+\frac{8D}{6v}+\frac{D}{6v}$$ $$\frac{24D}{6v}=\frac{4D}{v}$$
So the correct answer is A.

Vincen wrote:Marcia took a trip consisting of three segments at three different speeds: she drove a distance of (5D) at a speed of (2v), then a distance of (4D) at a speed of (3v), then a distance of D at a speed of (6v). In terms of D and v, what was the total time of Marcia's trip?

(A) 4D/v
(B) 4v/D
(C) (10D)/(11v)
(D) (10v)/(11D)
(E) (11D)/(10v)

The time for her first leg of the trip is 5D/(2v).

The time for her second leg is 4D/(3v).

The time for her last leg is: D/(6v).

Thus the total time is:

5D/(2v) + 4D/(3v) + D/(6v)

15D/(6v) + 8D/(6v) + D/(6v)

24D/(6v)

4D/v

Answer: A

Hi Vincen,

We're told that Marcia took a trip consisting of 3 segments at three different speeds: she drove a distance of (5D) at a speed of (2V), then a distance of (4D) at a speed of (3V), then a distance of D at a speed of (6V). We're asked for the total TIME of Marcia's trip in terms of D and V. This question can be solved by TESTing VALUES.

IF.... D=6 and V=1
1st Leg --> 30 miles at 2 miles/hour = 15 hours
2nd Leg --> 24 miles at 3 miles/hour = 8 hours
3rd Leg --> 6 miles at 6 miles/hour = 1 hour

Total Time = 15 + 8 + 1 = 24 hours. So we're looking for an answer that equals 24 when we TEST D=6 and V=1. There's only one answer that matches...

Final Answer: A

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Rich