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)

=>

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
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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.
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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.

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!