Jason must drive from his home to his office by one of two possible ro

Question

Jason must drive from his home to his office by one of two possible routes. If he must also return by one of these routes, what is Jason's average speed on a round trip from his home to his office?
 
(1) The longer route is 3 times the shorter route.
(2) Jason's average speed while driving to his office along the longer route was 50 miles per hour and his average speed while returing home along the shorter route was 60 miles per hour.

Diwakar003 · Answer

(1) The longer route is 3 times the shorter route. - Not sufficient
(2) Jason's average speed while driving to his office along the longer route was 50 miles per hour and his average speed while returing home along the shorter route was 60 - Not sufficient

(1) + (2)
Let x be the shorter distance and 3x be the longer distance.

Total time taken = (x/60) + (3x/50)

Average velocity = Total distance / Total time taken
= (4x) / (x/60) + (3x/50)
- Sufficient

Hence C.

Cheers!

rjg_25 · Answer

You're assuming it takes a short and a long route. He/she may take either the short or long route. Makes 3 different possible answers. 50 and 60 themselves are potential answers. Wouldn't you agree?

Advait01 · Answer

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

Bunuel · Answer

(2) Jason's average speed  while driving to his office along the longer route  was 50 miles per hour and his average speed  while returing home along the shorter route  was 60 miles per hour.

The intended meaning of the above is that Jason took the longer route to the office and the shorter route back home.

egmat · Answer

From Statement 2:
- Home → Office: He took the  longer  route at  50 mph 
- Office → Home: He took the  shorter  route at  60 mph

Why 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 mph

Test 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 mph

Same 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 mph

The 'd' cancels out completely, giving us one definite answer.

Answer: C

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