From Statement 2:
- Home → Office: He took the
longer route at
50 mph- Office → Home: He took the
shorter route at
60 mphWhy we don't need exact distances:When distances are in a fixed
ratio, the actual values cancel out in the average speed formula.
Let's prove it with numbers:
Test 1: Shorter route =
10 miles, Longer route =
30 miles- Total distance = 30 + 10 = 40 miles
- Total time = 30/50 + 10/60 = 0.6 + 0.167 = 0.767 hours
-
Average speed = 40 ÷ 0.767 = 52.17 mphTest 2: Shorter route =
60 miles, Longer route =
180 miles- Total distance = 180 + 60 = 240 miles
- Total time = 180/50 + 60/60 = 3.6 + 1 = 4.6 hours
-
Average speed = 240 ÷ 4.6 = 52.17 mphSame answer! The actual distance doesn't matter - only the ratio matters.Algebraically:Let shorter route = d, then longer route = 3d
Average Speed = Total Distance / Total Time
= (3d + d) / (3d/50 + d/60)
= 4d / (23d/300)
=
1200/23 mphThe 'd' cancels out completely, giving us one definite answer.Answer: CAdvait01
Shouldn't it be E as we don't know the exact route he took while A-B and B-A is same or not