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## Comment on

Devi and Mark## Hi Brent could you pls

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.

## You bet!

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

## Can this video also be solved

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

## That approach works, but only

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

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

## Perfect!

Perfect!

## Hi Brent. I understand the

## There's no way to determine

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

## When both travelers are

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

12/(51-36)

12/15= 4/5 hr= 48 minutes

## That's a perfectly valid

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