1/4" = 1' could be rewritten as 1:48.

1/4" = 1' could be rewritten as 1:48.
Think of it this way, there are (48) quarter inches in one foot.

From that I believe it should be easy to see that 1:48 is not the same as 1:150... but it is close to 1:50. You could make your measurement with the 1/4" scale and multiply your answer by 3.125 to get the number of feet.

If you scaled your pipe using the 1/4" scale, and the scale reads 10. Normally this would mean 10 feet, but in your case take 10 and multiply by 3.125 and you will get 31.25 feet.

That should work, you can double check my math on a known dimension... but you should be really careful when scaling any plan. Most plans specifically warn against scaling the plan and recommend only using dimensioned lengths that are given to you. If the length is not given it is always recommended to call the designer for a clarification.