Peter and Tom shared the driving on a certain trip. If Peter

since the time take by each is equal, it is straight respective distances: 2:5

Refer screenshot below:

Let Total Distance= 5
Peter drove= 2 mile and Tom Drove= 3 mile. Let, Each took 1 hour
Their speed = 2/1 : 3/1 = 2: 3

Let total distance be D.

Tom's covered distance is = 2D/5
Tom's rate= 2D/5T

Peter's covered distance = D-2D/5 = 3D/5
Peter's rate= 3D/5T

So Tom: Peter = 2D/5T x 5T/3D
= 2 : 3

Let the total distance = 5 miles, implying that Peter's distance = \(\frac{2}{5} * 5 = 2\) miles and that Tom's distance = \(5-2 = 3\) miles.
If Peter and Tom each drive for 1 hour, then Peter's speed : Tom's speed = 2 mph : 3 mph.

We can let the time driven by Peter and Tom = t. If we let the total distance = d, then Peter’s distance = (2/5)d = 2d/5 and Tom’s distance = (3/5)d = 3d/5.

Thus, Peter’s rate is (2d/5)/t = 2d/(5t), and Tom’s rate is (3d/5)/t = 3d/(5t).

The ratio of Peter’s average speed to Tom’s average speed is (2d/5t)/(3d/5t) = 10dt/(15dt) = 2/3.

Answer: E

Distance driven by Peter d(p) = 2/5
Distance driven by Tom d(t) = 1 - (2/5) = 3/5

Since time (T) taken is the same for Peter and Tom:

T(p) = T(t)
=> d(p) / s(p) = d(t) / s(t)
=> (2/5) / s(p) = (3/5) / s(t)
=> s(p) / s(t) = (2/3)
Answer is choice (E).

Asked: Peter and Tom shared the driving on a certain trip. If Peter and Tom both drove for the same amount of time, but Peter only drove 2/5 of the total distance, what was the ratio of Peter's average speed to Tom's average speed?

Since time is same for both Peter and Tom
d1/d2 = s1/s2 ;
where d1 & d2 are distance travelled by Peter and Tome respectively &
where s1 & s2 are speed of Peter and Tome respectively
(2/5)/(1-2/5) = (2/5)/(3/5) = s1/s2
s1:s2 = 2:3

IMO E

Bunuel, GMATNinja, can you please explain why Tom cannot drive the full distance s, and should drive 3/5 of the distance? What is the trigger in the questions?

If Tom drives the full distance S then Peter has nothing left to drive.

You've been given the distances both people drove in proportion to the total distance.

Let's assume that Peter and Tom drove for a total of "x" hours each. Since they both drove for the same amount of time, we can consider their driving time as equal.

Now, if Peter only drove 2/5 of the total distance, it means that Tom drove the remaining 3/5 of the distance.

Let's say the total distance of the trip is "d". Since Peter drove 2/5 of the distance, his driving distance would be (2/5)*d, and Tom's driving distance would be (3/5)*d.

Now, let's calculate the average speed for each of them.

Peter's average speed = Peter's driving distance / Peter's driving time = (2/5)*d / x = (2d)/(5x)

Tom's average speed = Tom's driving distance / Tom's driving time = (3/5)*d / x = (3d)/(5x)

To find the ratio of Peter's average speed to Tom's average speed, we can divide Peter's average speed by Tom's average speed:

(Peter's average speed) / (Tom's average speed) = [(2d)/(5x)] / [(3d)/(5x)] = (2d)/(3d) = 2/3

Therefore, the ratio of Peter's average speed to Tom's average speed is 2:3.

The answer is E. 2:3.

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