Does the tailwind component always have the same absolute value as the headwind component? If we are on course 360 and we have crosswind from 020 at 20 kts...does the amount of head wind on this leg equal the amount of tailwind on the reciprocal course (i.e. 180)?

To amplify the question with an example:


TAS:   260kts
Wind velocity: 310/35 kts


Given the above information, calculate ground speed on courses 240T and 060T.

When I use e6b+ aviation calculators, I get the following answers:


On a course of 240, the ground speed is 246kts. This is 14kts slower than the true airspeed.
On a course of 060, the ground speed is 270kts. This is 10kts faster
than the true airspeed.


Since I believe the headwind and tailwind components should be equal, the question is: why is there a difference of 4kts between the computed headwind component and the computed tailwind component
YES, If the "amount of headwind" was 10 knots due to the crosswind, then the "amount of tailwind" would also be 10 knots on the reciprocal course. 

BUT, because the 10 knot disadvantage with a head wind will last for a longer period of time than the 10 knot advantage with a tailwind, the entire trip will take longer and use more fuel than a trip in still air.

EXAMPLE: The headwind leg is 15 minutes longer, but the tailwind leg is only 10 minutes shorter, so you have a net loss of time.