# How to calculate a distance with different fraction ratios?

This is the math question for my sixth grader son. The answer is $136$ meters but could not figure it out. Can someone please explain how to solve it. Thank you.

Adam first walks $3/8$th of a road. He then walks $2/8$th and $2/3$rd of the road. Since Adam still has $17$ meters to walk. How long is the total journey? (Answer: $136$m)

• Something looks fishy. Is he reversing course? Because $\frac{3}{8} + \frac{2}{8}$ is greater than 50% of the road, as is $\frac23$. Are you sure you transcribed the fractions properly? Commented Jan 2, 2015 at 15:54
• That is exactly what's on the paper.
– Ann
Commented Jan 2, 2015 at 15:57
• Then something must be afoul, because $\frac{3}{8}+\frac{2}{8} = \frac{5}{8} = .625$. So the first two legs cover 62.5% of the distance. The third leg covers about 66.7% of the distance. So the problem, as stated, suggests that Adam walks more than 100% of the road yet still has more road to go. Either Adam's real name is Sisyphus, or the problem is broken. Commented Jan 2, 2015 at 15:59
• In fact, $\frac{3}{8}+\frac{2}{3}$ is greater than 100% by itself. Commented Jan 2, 2015 at 16:08
• Note: $17 = \frac{136}{8}$. However I agree with @Arkamis, it doesn't make sense as it is but perhaps the last 2/3rd are in fact 3/8th. Or perhaps there's a '2/3rd of the remaining distance' or something like that somewhere in the question. Commented Jan 2, 2015 at 16:15

The question is incorrect as the commentators have shown. If the last $2/3$ should be $2/8$, he has walked $7/8$ of the road and has $1/8$ left, which we are told is $17$ meters. That says the whole road is $8 \times 17=136$ meters, the stated answer.
• Nice catch. I wonder if this is an artifact of a "copy of a copy of a copy..." making an $8$ look like a $3$. Commented Jan 2, 2015 at 16:17