A car overtakes an auto at point A at 9 am. The car reaches point B at

Question

A car overtakes an auto at point A at 9 am. The car reaches point B at 11 am and immediately turns back. It again meets the auto at point C at 11:30 am. At what time will the auto reach B?

A. 12:35 pm
B. 12:40 pm
C. 12:45 pm
D. 12:50 pm
E. 12:55 pm

CareerGeek · Answer

Let the speeds of car and auto be ‘c’ & ‘a’ respectively and the distance between A & B be ‘d’ and that of between B & C be ‘x’

To find: time taken by auto to reach B = d/a

Distance traveled by car from A to C = c*2.5 (9:00-11:30 am)
—> d + x = 2.5c ....... (1)
Distance traveled by auto from A to C = a*2.5
—> d - x = 2.5a ........ (2)
Also, car traveled from A to B in 2 hours
—> d = c*2 
—> d = 2c ....... (3)

(1) / (3) 
—> (d + x)/d = 2.5c/2c = 2.5/2 = 5/4
—> 4d + 4x = 5d
—> d = 4x 
—> x = d/4
Substitute value of x in (2),
—> d - d/4 = 2.5a
—> 3d/4 = 5/2a
—> d/a = 5/2*4/3 = 10/3 or 3 1/3 hours (1/3 hours = 1/3*60 = 20 minutes)
—> d/a = 3 hours 20 minutes

—> Time when auto reaches point B = 9:00 + 3:20 = 12:20 pm

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stne · Answer

A---------------------------B
9:00 am \hspace{10mm} x \hspace{10mm}   11:00 am

Let the distance from the point of overtaking A to point B be  x 
Let  c  be speed of car and  a  be speed of Auto.
In 2 hours car reaches B so  2c = x  , (1)
also in 2 Hours Auto travels  2a

Now car turns back from point B and in half an hour (30 min ) it travels  \frac{1}{2}c 
Also during this half an hour Auto travels  \frac{1}{2}a  
so we have  2a+\frac{1}{2}a +\frac{1}{2}c= x \rightarrow 5a+c=2x ..(2)

We need  \frac{x}{a}   -> where  x  is required distance and  a  is Auto's speed

from (1) we have  2c = x  or  c=\frac{x}{2}  putting the value of c in (2)
 5a+c=2x 
 5a+\frac{x}{2} =2x 
 10a=3x

\frac{x}{a} =\frac{10}{3}  -> 3 hr 20 min , hence 3 hr 20 min after 9:00 AM Auto will reach point B , so Auto will reach point B at 12:20 PM.

Also getting 12:20 PM , but the same not available among the options !

Hope this helps.

neha283 · Answer

Hi, 
how did you come to equation (2) , could you explain it a little more?

Thanks!

stne · Answer

Hi  neha283 ,

Total distance between point A and B is  x

Auto's speed is less than Car's speed so in 2 hours when Car reaches point B Auto does NOT reach point B. Auto is somewhere in between A and B. At a distance of  2a .

Now Car starts returning from B and in half an hour meets auto.In this half an hour Auto has also moved towards B by a distance of further  \frac{1}{2}a .

So when Car meets Auto total distance traveled by Auto and car is  x :
 
Distance traveled by car in half an hour  \frac{1}{2}c  ( Note : Car is returning from B well as Auto is still going towards B )
Distance traveled by auto in 2 hours + distance traveled by auto in half an hour ->
 2a+\frac{1}{2}a +\frac{1}{2}c= x  (2)

Hope its more clear now.

ScottTargetTestPrep · Answer

Solution:

Let c = speed of the car and a = the speed of the auto. We see that it takes 2 hours for the car to drive from A to B; thus, the distance from A to B, in terms of c, is 2c. Similarly, on the return trip, it takes 30 minutes, or 0.5 hour, for the car to meet the auto at C, by which time the auto has driven for 2.5 hours. Thus the distance from A to B, in terms of a and c is 2.5a + 0.5c. Since the distance from A to B is the same no matter how we express it, we can create the equation:

2c = 2.5a + 0.5c

1.5c = 2.5a

a = 1.5c/2.5 = 15c/25 = 3c/5

Since the distance from A to B is 2c and the auto’s speed is a = 3c/5, it will take the auto 2c/(3c/5) = 2c x 5/(3c) = 10/3 = 3 ⅓ hours or 3 hours and 20 minutes to drive from A to B. Since the auto is at point A at 9 am, it will be at point B at 12:20 pm.

Alternate Solution:

Let the distance between C and B be d. Notice that it took half an hour for the car to travel from B to C, and it took 2 hours for the same car to travel from A to B; therefore, the distance between A and B is four times the distance between C and D; i.e. 4d. Thus, the distance between A and C is 4d - d = 3d.

It took the auto 2.5 hours = 150 minutes to drive a distance of 3d. Thus, to drive from C to B (a distance of d), it will take the auto 150/3 = 50 minutes. Since the auto was at point C at 11:30, it will arrive at point B at 11:30 + 50 minutes = 12:20pm.

Answer: Not Given

Bentsi · Answer

Bunuel 
Can you please help us here?

bumpbot · Answer

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A car overtakes an auto at point A at 9 am. The car reaches point B at

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