Ann and Bob drive separately to a meeting. Ann s average driving speed

Question

Ann and Bob drive separately to a meeting. Ann s average driving speed is greater than Bob's average driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?

A. 8:3
B. 3:2
C. 4:3
D. 2:3
E. 3:8

A. 8:3
B. 3:2
C. 4:3
D. 2:3
E. 3:8

My approach is given below
Rb = X mph
Db = 2 * Da miles = 2Y miles
Db = Rb * Tb
Tb = Db/Rb
 = 2Y/X

Ra = 1/3 of Rb mph = X + X/3 = 4X/3 mph
Da = Y miles
Da = Ra * Ta
Ta = Da/Ra
 = Y/(4X/3) = 3Y/4X

Ta/Tb = 3Y/4X * X/2Y
 = 3/8
Ta:Tb = 3:8

My answer does not match the answer in the solution.

Bunuel · Answer

The red part is not correct, since Ann drives twice as many miles as Bob it should be Db = Da/2 miles = Y/2 miles.

Also you used a lot of unnecessary variables to solve this question.

Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.

The ratio of Ann's time to Bob's time is 3:2.

Answer: B.

Hope it helps.

sashiim20 · Answer

Let Distance traveled by Bob be  = D

Distance traveled by Ann  = 2D

Let Speed of Bob  = S

Speed of Ann  = S + \frac{1}{3}S = \frac{3S + S}{3} = \frac{4}{3}S

Let Time traveled by Ann  =T1

Time traveled by Bob  = T2

Ratio of time traveled by Ann to time traveled by Bob  = \frac{T1}{T2}

T1 = \frac{Distance}{Speed} = \frac{2D}{(4/3)S} = \frac{6D}{4S} = \frac{3D}{2S}

T2 = \frac{Distance}{Speed} = \frac{D}{S}

T1/T2 = (3D/2S) / (D/S) = \frac{3D}{2S} * \frac{S}{D} = \frac{3}{2}  or  3 : 2

Answer B

gurmukh · Answer

Ann Bob
Speed 4 3
Distance 2 1
Time 2/4 1/3
 1/2 1/3
 3 2
Option B is the answer

Posted from my mobile device

CrackverbalGMAT · Answer

Since the question provides data about the ratio of the speeds and the distances, it’s a good idea to work with the ratios given.

Ann’s average speed is greater than Bob’s average speed by  \frac{1}{3} rd of Bob’s average driving speed. For example, if Bob’s average speed is 3 mph, Ann’s average speed is 4 mph.

\frac{Speed of Ann }{ Speed of Bob}  =  \frac{4}{3} . Let’s say these speeds are 4x and 3x mph respectively

Ann drives twice as many miles as Bob i.e. Ann = 2 * Bob.

\frac{Distance by Ann }{ Distance by Bob}  =  \frac{2}{1} . Let’s say these distances are 2y and y miles respectively.

Time taken =  \frac{Distance }{ Speed}

Time taken by Ann =  \frac{2y }{ 4x}  hours and Time taken by Bob = \frac{ y }{ 3x}  hours.

Therefore, ratio of time taken by Ann and Bob =  \frac{2y }{ 4x}  *  \frac{3x }{ y}  =  \frac{3}{2}  or 3:2.

The correct answer option is B .

Hope that helps!

laborumpossimus · Answer

I tried plugging in numbers like assuming bbos speed as 60 
And a,s speed as 80 
And took 240 as distance for a and 
120 miles as distance for b 
Is this approach appropriate?

Bunuel · Answer

Yes, that approach is correct.

Bob’s speed = 60 mph
Ann’s speed = 80 mph, which is 1/3 greater than 60

Bob’s distance = 120 miles
Ann’s distance = 240 miles, which is twice Bob’s distance

Then:

Bob’s time = 120/60 = 2 hours
Ann’s time = 240/80 = 3 hours

So the ratio of Ann’s time to Bob’s time is:

3:2

Answer: B.

egmat · Answer

Hi laborumpossimus,

Good news: your approach is  completely valid , and it actually gives the right answer. Let me walk through your own numbers so you can see it.

You chose:
- Bob's speed =  60 , Ann's speed =  80  - check: 80 = 60 + 1⁄3·60 = 60 + 20 ✓
- Ann's distance =  240 , Bob's distance =  120  - check: 240 = 2 × 120 ✓

Both conditions in the question are satisfied, so your picks are legal. Now just compute the times:
- Bob's time = 120 ÷ 60 =  2  hours
- Ann's time = 240 ÷ 80 =  3  hours

Ratio of Ann's time to Bob's time =  3 : 2  - answer  B . So your method didn't just "work," it lands exactly on the official answer.

The one rule for plugging in

The only thing you must guarantee is that your chosen numbers obey  every  constraint at once - which yours do. As long as that holds, you'll get the same ratio no matter what specific numbers you pick.

Notice that's exactly why Bunuel's smaller numbers (Bob:  3  mph,  6  miles; Ann:  4  mph,  12  miles) give the same  3 : 2 . The actual values wash out - only the  ratio  survives - which is what makes plugging in safe for this kind of question.

Quick way to trust it:  try one more legal set, say Bob =  30  mph over  90  miles, Ann =  40  mph over  180  miles. Bob's time =  3  hr, Ann's time =  4.5  hr -  4.5 : 3  =  3 : 2  again. Same answer every time.

So keep using this approach - just always double-check that each chosen number respects all the given relationships before you compute.

Answer: B

Ann and Bob drive separately to a meeting. Ann s average driving speed

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Ann and Bob drive separately to a meeting. Ann s average driving speed

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