Problem Solving

Hi All,

We're told that a plane traveled K miles in its first 96 minutes of flight time and it completed the remaining 300 miles of the trip in T minutes. We're asked for the average speed of the plane, in miles per hour, for the entire trip. This question can be solved by TESTing VALUES.

IF... K = 300 and T = 96...
then the plane traveled 300+300 = 600 miles in 96+96 = 192 minutes

We're asked for the average speed in miles/HOUR though, so we have to go the extra step of converting minutes to hours. This can be done in a couple of different ways: either by dividing 192 by 60 OR by multiplying the fraction (600/192) by 60. If you take the second approach, then you can actually avoid the physical math and just look for the answer that matches the 'look' of the fraction: 60(600/192). There's only one answer that matches...

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:Source: Veritas Prep

A plane traveled k miles in its first 96 minutes of flight time. If it completed the remaining 300 miles of the trip in t minutes, what was its average speed, in miles per hour, for the entire trip?
$$A.\ \frac{60\left(k+300\right)}{\left(96+t\right)}$$
$$B.\ \frac{\left(kt+96\left(300\right)\right)}{96t}$$
$$C.\ \frac{\left(k+300\right)}{60\left(96+t\right)}$$
$$D.\ \frac{5k}{8}+\frac{60\left(300\right)}{t}$$
$$E.\ \frac{5k}{8}+5t$$
The OA is A

We are given that a plane traveled k miles in 96 minutes. Since we need the average speed in miles per hour we can convert 96 minutes to hours.

96 minutes = 96/60 = 8/5 hours

We are also given that the plane completed the remaining 300 miles in t minutes. We must also convert t minutes to hours.

t minutes = t/60 hours

Now we can calculate the average speed for the entire trip, using the formula for average speed.

Average speed = total distance/total time

Average speed = (k + 300)/(8/5 + t/60) = (k + 300)/(96/60+t/60)

Average speed = (k + 300)/((96 + t)/60)

Average speed = 60(k + 300)/(96 + t)

Answer: A