delta23 wrote:

Jack drove from Point A to Point B at a rate of 1.2 minutes per kilometer. He then drove back to Point A from Point B, along the same route, at 1 minute per kilometer. If he took anywhere between 3 hours to 5 hours to travel from Point A to Point B and between 2 hours to 3 hours on his way back, what could be the distance between the two points?

A) 140 kilometers

B) 160 kilometers

C) 200 kilometers

D) 220 kilometers

E) 270 kilometers

Two possible traps here:

1) min/max distance; and

2) distance is ONE way ("between ... A and B")

Leg 1: from A to B

Rate: \(\frac{1km}{1.2mins}*\frac{50}{50}=\frac{50km}{60mins}=\frac{50km}{1hr}\)

Distance? He drove between 3 and 5 hours

\(\frac{50km}{hr}*3hrs=150\) kms

\(\frac{50km}{hr}*5hrs=250\) kms

\(150 \leq D \leq 250\) kms

Leg 2: from B to A

Rate: \(\frac{1km}{1min}=\frac{60km}{60mins}=\frac{60km}{1hr}\)

Distance? He drove between 2 and 3 hours

\(\frac{60km}{hr}*2hrs=120\) kms

\(\frac{60km}{hr}*3hrs=180\) kms

\(120 \leq D \leq 180\) kms

For Leg 1 the MINIMUM distance is 150 kms, because the minimum

time is 3 hours.

3 hours' distance of 150 kms "wins" over Leg 2 minimum of 120 kms. (Distance depends on time traveled, and time is defined strictly for each leg.)*

The distance between A and B cannot be less than 150 km.

For Leg 2, from B to A, the MAXIMUM distance is 180 kms. The distance from B to A (=A to B) cannot be greater than 180 km

He traveled at least 150 km and at most 180 km: \(150< D<180\) kms

Only 160 kms fits in that range

Answer B

*Track on time to decide minimum and maximum

Minimum

-- the least time for Leg 1 is 3 hours

-- The least time Leg 2 is 2 hours

-- He cannot travel 2 hours for Leg 1

3 hours (+ corresponding distance at rate in Leg 1) "wins."

Minimum distance is 150

Maximum

-- The most time in Leg 2 is 3 hours

-- The most time in Leg 1 is 5 hours

-- He cannot travel 5 hours during Leg 2

3 hours (+ corresponding distance at rate in Leg 2) "wins."

Maximum distance is 180 km
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that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"