How many degrees are between the hands of a clock at 3:40?

Question

(A) 150°

(B) 140°

(C) 130°

(D) 125°

(E) 120°

pushpitkc · Answer

Every hour will translate to 30°.
At 3:40, the hour and minute hand would be separated by 5*30° = 150° (without considering the hour hand's advancement)

At 40 minutes past any hour, the hour hand will be  \frac{2}{3}*30° = 20°  degree away from the hour line.

Therefore, the degree between the hour hand and the minute hand is 150° - 20° = 130° (Option C)

gracie · Answer

40- =21 2/3 minutes
21 2/3*6°=130°

Fdambro294 · Answer

Method 1:

Start from the position of 3 PM and act as if the Minute Hand and Hour Hand move separately to make the visualization/calculation easier.

At 3 PM:

Minute hand will be directly on the 12

Hour hand will be directly on the 3

There is a 30 degree gap between each of the 12 “ticks” on the clock. (360 degrees / 12 gaps)

Therefore, at 3 PM, there is a 90 degree angle between the Minute Hand on 12 and the Hour Hand on 3.

40 minutes pass. (1st) move the Minute Hand and pretend the Hour Hand doesn’t move.

In 1 minute ————> the Minute Hand will travel 6 degrees.

Therefore in 40 minutes ———>the minute hand will travel (40) (6) = 240 Degrees

The minute hand must first travel past the 90 degrees “gap distance” it is behind the hour hand.

And then the minute hand will be (240) - (90) = 150 degrees ahead of the hour hand

(2nd) now we can move the hour hand

In 1 minute —————> the hour hand will move (1/2) degree

Thus in 40 minutes ————> the hour hand will move 20 degrees

The hour hand will cut down 20 degrees of this 150 degree “lead” that the minute hand has on the hour hand.

(150) - (20) = 130

Answer: 130 degrees

Or

Method 2:
Remember that for each minute that passes, the relative speed of:

(minute hand) - (hour hand) = 5.5 degrees each minute

***they are moving in the same direction so the relative speed is not added, but subtracted

At 3 PM there is a 90 degree gap distance between the 2 hands (the minute hand has to “catch up” 90 degrees to meet the hour hand)

In 40 minutes:

(5.5) (40) = 220 degrees is traveled

However, 90 degrees of this was the minute hand “catching up” to the hour hand

220 - 90 = 130 degrees

Answer: 130 degrees

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iridescent995 · Answer

we can directly use a formula for this to save time...

(11m - 60h)/2 (m is minutes, h is hours)

=> (11 * 40 - 60 *3 )/ 2 =>130

JeffTargetTestPrep · Answer

Minute hand:

Since one minute corresponds to a central angle of 360/60 = 6 degrees, 40 minutes corresponds to 40 × 6 = 240 degrees.

Hour hand:

Since one hour corresponds to 360/12 = 30 degrees, 3 hours and 40 minutes, which is equal to 11/3 hours, corresponds to 30 × 11/3 = 110 degrees.

So, the degree difference between the hands is:

240 – 110 = 130 degrees

Answer: C

(Note: Actually, the two hands determine another central angle, which is 360 – 130 = 230 degrees.)

Archit3110 · Answer

Formula
11/2 × minute - 30x hour
5.5×40 -(30*3)
130
Option C

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How many degrees are between the hands of a clock at 3:40?

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How many degrees are between the hands of a clock at 3:40?

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