Alice and Bob traveled in the same direction along the same route at t

Question

Alice and Bob traveled in the same direction along the same route at their respective constant speeds of 12 km per hour and 6 km per hour. They each started to travel from their own houses. Bob’s house is halfway between Alice’s house and the destination. After passing Bob, Alice took 10 minutes to reach the destination. How many minutes did it take Bob to reach the destination after Alice passed him?

A. 5 min 
B. 6 min 
C. 8 min 
D. 10 min 
E. 20 min

Hatakekakashi · Accepted Answer

Since the speed of Alice is double the speed of bob, the time taken by alice is half the time taken by Bob

Alice takes 10 mins thus bob takes  \frac{10}{1/2}  = 10 x2 = 20

(E)

generis · Answer

Convert rates to minutes.
A's rate in minutes: 
  \frac{12km}{1hr}=\frac{12km}{60mins}=\frac{1km}{5mins}

B's rate in minutes: 
  \frac{6km}{1hr}=\frac{6km}{60mins}=\frac{1km}{10mins}

Information to ignore or avoid:
1) Bob's house as a halfway point
2) Relative speed
3) Whatever happens before the passing point

As soon as Alice passes Bob, the chase is over. Both travel  the same distance  to the end.*

We need only two pieces of information:

1) the distance from pass point to end, which we can derive from Alice's time; and

2) the time it takes for Bob to travel that distance, which we can derive from his rate

Distance to end 
In 10 minutes, the distance Alice covers is
 D= R*T , so 
 D= \frac{1km}{5mins}* 10mins = 2  kms

Time  Bob takes to cover distance of 2km
 R*T= D , so  T =\frac{D}{R}

T =\frac{2km}{\frac{1km}{10mins}}=(2km*\frac{10mins}{1km})= 20  minutes

Answer E

* Distance from pass point to end is same for both
Point at which A passes B
 House B --->---B|------------|
 House B ---->--A|------------|

A is in front of B
 House B --->--->|B->---------|
 House B ---->-->|-----A-->---|

MathRevolution · Answer

=>

After Alice passed Bob, she traveled for  10  more minutes.
Since Bob’s speed is half of Alice’s speed, he took a further  20  minutes to reach the destination.

Therefore, the answer is E.

Answer: E

sameeruce08 · Answer

If bob house is halway between alice and destination and if slice speed is twice that of bob

How are they supposed to cross each other they will meet directly at destination

alice has to cover 2d distance with 12km/hr implies time taken is 2d/12=d/6

bob jas to travel d with speed 6km/hr hence time taken is d/6

so they meeet directly in destination

please explain

generis · Answer

sameeruce08  , the "halfway" info is to let us know that Alice starts behind Bob.

As far as distance:
Alice does travel 2d, but we don't care about that because we don't know start times.

After she passes him, both travel same distance.

We find distance from her rate and time. In minutes. (Or fraction of hour.)

Then find Bob's time from distance and rate.

All that matters: separate rates and times.

She travels at 12 km per hour.
One hour = 60 minutes.
Rate: She travels 12 km in 60 minutes: 
D=  (\frac{12km}{60mins}*10 minutes) = 2 kms

Bob's speed = 6 km/hr, OR 6 km in 60 minutes.

Bob's time?
 T = \frac{D}{R} 
 T=\frac{2}{(\frac{6}{60})}=(2*\frac{60}{6})=20  mins

OR get time from Bob's unit rate =  \frac{6km}{60mins} =\frac{1km}{10mins}

To go 2 km, at a rate of 1 km per 10 minutes, it will take him 2 * 10 = 20 minutes.

Hope that helps.

pravalithota · Answer

After crossing Bob, Alice will travel 10(min)x12(km/hr)
And this distance is constant and Bob also will travel the same distance in x(min)x6(km/hr)
equating, x=20min
Answer: E

coylahood · Answer

In order to arrive at the correct answer we need to consider the distance that Alice will cover in 10 minutes after catching up with Bob. At 12km per hour, Alice will cover a distance of 10/60 x 12 = 2km.
Having calculated the distance, we can used this figure to calculate the time that it would take Bob to cover 2km
At a speed of 6km per hour, Bob will cover 2km in 2/6 x 60 = 20 minutes. 
Therefore, the correct answer is E.

PinakiRDas · Answer

Are we assuming that they didn't start at the same time and Bob started only when Alice crossed his house?

fauji · Answer

Nope. They both started at same time. Since Bob's house is halfway between Alice's house and destination..and Alice being 2x(12kmph) faster than bob is... Alice would have crossed bob somewhere between bob's house and destination. Given in the question is the time Alice took AFTER crossing bob and ask is for time taken by bob to reach destination after alice crossed.

Hope it helps!

PinakiRDas

Are we assuming that they didn't start at the same time and Bob started only when Alice crossed his house?

Hope it helps!

Kinshook · Answer

Given: 
1. Alice and Bob traveled in the same direction along the same route at their respective constant speeds of 12 km per hour and 6 km per hour. 
2. They each started to travel from their own houses. 
3. Bob’s house is halfway between Alice’s house and the destination. 
4. After passing Bob, Alice took 10 minutes to reach the destination.

Asked: How many minutes did it take Bob to reach the destination after Alice passed him?

3. Bob’s house is halfway between Alice’s house and the destination.

Alice House -----------------x km -----------------Bob's House ---------------------x km ------------------------Destination

4. After passing Bob, Alice took 10 minutes to reach the destination. 
Distance travelled by Alice = (10 /60) * 12 = 2 km
Time taken by Bob to cover 2 km = 2/6 hr = 20 mins

IMO E

Sheelarani · Answer

But in 10 mins when Alice walking from his home to Bob's home, Bob would also be walking towards the destination and must have covered some distance. while Alice covered 2km in 10 mins after passing Bob's home, Bob must also have covered some distance between his house and destination. Then why are we not considering that already covered distance?

bumpbot · Answer

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Alice and Bob traveled in the same direction along the same route at t

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