A car is 40 miles behind a bus, which is traveling in the same

Question

A car is 40 miles behind a bus, which is traveling in the same direction along the same route as car. After how much time will the car be at a distance 8 miles from the bus?

(1) The car is traveling at a constant speed of 48 miles per hour. 
(2) The bus is traveling at a constant speed of 32 miles per hour.

SaquibHGMATWhiz · Accepted Answer

I believe this is a question from one of our WWW webinars.

The trick here is to understand that the distance of 8 km can happen in two different ways.

1. When the car is behind the bus.
2. When the car is ahead of the bus.

Hence, even knowing relative velocity won't help.

The answer is E.

Suruchim12 · Answer

SaquibHGMATWhiz  Hi,

Can you please explain this a little more.

SaquibHGMATWhiz · Answer

Did you try to visualize the setup? Because that will be important to understand the trap.

We do not know whether the car has overtaken the bus or not.
We know the initial distance was 40 km and in the end, it is 8 km. 
 There could be two scenarios here.

1. The car has overtaken the bus. So it is ahead of the bus. In such a scenario the relative distance covered by the car is 40 + 8 = 48 km. 
The visual representation can be as follows:
Initial, (Traveling direction ---->) Car_________________________Bus
Final, (Traveling direction ---->) __________________________________Bus_______Car
Since we know the relative speed is 16 km/h so we can say that it would take  \frac{48}{16} = 3  hours

2. The car has NOT overtaken the bus yet. So it is still behind the bus. In such a scenario the relative distance covered by the car is 40 - 8 = 32 km. 
Initial, (Traveling direction ---->) Car_________________________Bus
Final, (Traveling direction ---->) __________________________________Car_______Bus
Since we know the relative speed is 16 km/h so we can say that it would take  \frac{32}{16} = 2  hours

Regards!

pappal · Answer

good one!  I got trapped in that whether the car is 8 miles behind the bus or 8 miles ahead of the bus. 
which will give two different values of the time required so not sufficient together even.
also its very clear that individual statements aren't sufficient alone.
so E

roshaun25 · Answer

Doesn't "After how much time" imply that it's referring to the first time the car is within 8 miles from the bus? It's not asking "at what point in time", or it would be more open ended to allow both possibilities

Bunuel · Answer

“After how much time” just means “how long until the condition happens,” but it does not say “the first time” or “before the car passes the bus.”

egmat · Answer

The question asks: "at a distance  8 miles from  the bus"

"Distance from" doesn't specify direction.  It just means the gap between car and bus is 8 miles.

Using both statements: 
- Car speed:  48 mph 
- Bus speed:  32 mph 
- Car gains:  16 mph  on the bus
- Initial gap:  40 miles

Case 1:  Car is  8 miles behind  (gap shrinks from 40 to 8)
→ Car closes  32 miles  → Time = 32/16 =  2 hours

Case 2:  Car is  8 miles ahead  (car passes bus, then pulls ahead by 8)
→ Car travels  48 miles  relative to bus → Time = 48/16 =  3 hours

Both are valid interpretations of "8 miles from the bus."

If the question wanted only the first scenario, it would say "8 miles  behind  the bus." Since it says "8 miles  from " - which is just a distance with no direction - we cannot determine which interpretation is intended.

A car is 40 miles behind a bus, which is traveling in the same

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A car is 40 miles behind a bus, which is traveling in the same

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