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A man covered 1 3 of the distance to his destination at 20 miles per h
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26 Jan 2024, 00:35

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A man covered 1/3 of the distance to his destination at 20 miles per hour, 1/2 of the remaining distance at 12 miles per hour and remaining distance at 40 miles per hour. Which of the following statements is true regarding the entire journey?

Indicate all possible statements.

(A) Time taken to travel the part of the distance at 40 miles per hour was 1/2 of the time taken to cover the part of the distance at 20 miles per hour.

(B) Total time taken to complete the entire journey was 18 hours.

(C) Average speed for the entire journey is 20 miles per hour.

Indicate all possible statements.

(A) Time taken to travel the part of the distance at 40 miles per hour was 1/2 of the time taken to cover the part of the distance at 20 miles per hour.

(B) Total time taken to complete the entire journey was 18 hours.

(C) Average speed for the entire journey is 20 miles per hour.

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A man covered 1 3 of the distance to his destination at 20 miles per h
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26 Jan 2024, 16:29

1

There's no mention of actual distance, only of actual rates. That means we can't determine actual total time, which rules out (B).

Let's say actual total distance = 360.

Distance traveled at 20mph \(= \frac{1}{3} * 360 = 120\)

1/2 the remaining distance \(\frac{1}{2} * (360 - 120) = 120\)

The remaining distance \(= 360 - (120+120) = 120\)

Let a = Time taken to travel the part of the distance at 20 mph, b = Time taken to travel the part of the distance at 12 mph, and c = Time taken to travel the part of the distance at 40 mph.

Using the distance-rate formula, t = d/r :

\(a = 120 / 20 = 6\)

\(b = 120 / 36 = \frac{10}{3}\)

\(c = 120 / 40 = 3\)

Since c = 1/2a, (A) is correct.

The average speed for the entire journey = \(\frac{360}{6 + \frac{10}{3} + 3} = 18.95\), so (C) is incorrect.

Let's say actual total distance = 360.

Distance traveled at 20mph \(= \frac{1}{3} * 360 = 120\)

1/2 the remaining distance \(\frac{1}{2} * (360 - 120) = 120\)

The remaining distance \(= 360 - (120+120) = 120\)

Let a = Time taken to travel the part of the distance at 20 mph, b = Time taken to travel the part of the distance at 12 mph, and c = Time taken to travel the part of the distance at 40 mph.

Using the distance-rate formula, t = d/r :

\(a = 120 / 20 = 6\)

\(b = 120 / 36 = \frac{10}{3}\)

\(c = 120 / 40 = 3\)

Since c = 1/2a, (A) is correct.

The average speed for the entire journey = \(\frac{360}{6 + \frac{10}{3} + 3} = 18.95\), so (C) is incorrect.

gmatclubot

A man covered 1 3 of the distance to his destination at 20 miles per h [#permalink]

26 Jan 2024, 16:29
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