Question: Devi and Mark

Comment on Devi and Mark

Hi Brent could you pls explain the below problem

An executive drove from home at an average speed of 30 mph to an airport where a helicopter was
waiting. The executive boarded the helicopter and flew to the corporate offices at an average speed of
60 mph. The entire distance was 150 miles; the entire trip took three hours. Find the distance from the
airport to the corporate offices.
gmat-admin's picture

You bet!

Let t = time (hours) spent driving to airport
So 3-t = time spent flying

(distance to airport) + (distance flying) = 150 miles
distance = (rate)(time)

So, 30t + 60(3-t) = 150
Expand: 30t - 180 - 60t = 150
Solve: t = 1

So, the executive spent 1 hour driving and 2 hours flying

Flying distance = (60 mph)(2 hours) = 120 miles

Very clear explanation, thank you!

Can this video also be solved algebraically with the below method?

Using the formula D = RT, we know that
Devi: D = 36T (36 mph)
and Mark: D = 51(T-20) --> T-20 since we know Devi is 20 min ahead of Mark

Make the two equations equal to each other to see when they'll meet, and solve for T, which equals 68. 68 + 1:00pm = 2:08pm. Answer is E
gmat-admin's picture

That approach works, but only because the answer to the question depends on relative speeds (i.e., Mark's speed is 51/36 times Devi's speed.

I say this because, in your solution, you use the fact that D = RT
Then you say that, for Devi, D = 36T (36 mph)
This is true AS LONG AS T = Devi's travel time in HOURS (since her speed is given in miles per HOUR)

However, in your next step, you say that for Mark, D = 51(T-20)
Here, the 20 represents 20 MINUTES (not 20 hours).
This can create issues since you have Mark's speed as 51 miles per HOUR

However, as I said, this small issue has no effect on the solution, since the answer depends on relative speeds.

However, that mistake COULD easily get you into trouble with other questions.

With respect to the unit issue can we solve with

36T = 51(T-1/3) (I used 1/3 hours for 20 mins since the speed is in MPH)
-15T = -17
T = 17/15
17/15 * 60 = 17 * 4 = 68 minutes
gmat-admin's picture

Perfect!

Hi Brent. I understand the calculation, but isnt Mark's travel time of 48 minutes the TOTAL time it takes him to cover the total distance from Townsville to Villageton? Or is this the time it takes him to catch up? Could you pls explain why its not the TOTAL time of the trip vs ONLY the time it takes him to catch up with Debbie? Thanks
gmat-admin's picture

There's no way to determine Mark's travel time to reach Villageton, since we don't know the distance to Villageton.

In fact, the part about Mark traveling TOWARDS Villageton is irrelevant. I could have also framed the question to say that Devi and Mark both left Townville and are traveling EAST along the same road.

The 48 minutes is the time it takes Mark to catch up with Devi.
In other words, it take Mark 48 minutes to decrease the gap (between him and Devi) from 12 miles to 0 miles.

Does that help?

Cheers,
Brent

Thanks Brent. Say if they were coming from OPPOSITE directions, then if I do this using the Distance formula, would the solution be the same? When we are equating the DISTANCE of both parties, what are we in effect saying? I am confused about that part in the question. Why are we equating the distances of both parties?
gmat-admin's picture

When both travelers are traveling in the same direction, then the traveler who is closing the gap will catch up to the other traveler when both travelers have traveled the same distance.

That is, when the gap is closed and both travelers are TOGETHER, we know that, at that moment, they have both traveled the same distance (since they both left from the SAME LOCATION and since they are not TOGETHER)

As for your other question (when they are coming from OPPOSITE directions), we CANNOT say that, when they meet, they have traveled the same distance.

Consider this example:
Let's say you and I are 1000 km apart.
You start walking towards me at a speed of 1 km per hour.
It start running towards me at a speed of 1000 km per hour.
When we meet, I would have traveled almost 1000 km, and you would have traveled less than 1 km.
So, our distances traveled would NOT be equal.

However, we CAN say one thing about what happens when the travelers are coming from OPPOSITE directions. We can say that, when they meet, their COMBINED travel distances will equal the total distance they were apart when they first started.

So, in the above example (when you and I start 1000 km apart), we can say that, when we MEET, the distance you have traveled PLUS the distance I have traveled EQUALS 1000 km

Does that help?

Cheers,
Brent

Yes thanks so much!

hey! Can I say that after 20 minutes, Devi traveled 12 miles, so the time would be distance/ speed i.e.
12/(51-36)
12/15= 4/5 hr= 48 minutes
gmat-admin's picture

That's a perfectly valid solution, Saahithi (in fact it's identical to my first solutions, which ends at 2:50 in the video :-)

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