A fly and a train are moving towards each other along a straight rail

Question

A fly and a train are moving towards each other along a straight rail track. If the train remained stationary, the fly would reach the train in 4 hours. If the fly remained stationary, the train would hit it in 3 hours. Both the fly and the train started moving at the same time towards each other. After one hour and 20 minutes of flight, the fly will stop and remain stationary at its new position. The train will continue to move towards the fly at its usual speed. How long after the journey began will the train hit the fly?

(A) 1/9 hour
(B) 2/3 hour
(C) 7/9 hour
(D) 4/3 hour
(E) 2 hours

(A) 1/9 hour
(B) 2/3 hour
(C) 7/9 hour
(D) 4/3 hour
(E) 2 hours

Mathias9777 · Answer

E - 2 hrs.

We can assume that the distance between them are 120 km (goes easily with 30 and 40)

r*t=D
Fly: 30 * 4 hrs = 120 km
Train: 40 * 3 hrs = 120 km

Fly spends 1 hr and 20 min before stopping. This equals 40 km (30 * 1 1/3 = 40).

Train therefore travels a total of 120 - 40 = 80.

This the train spends (D/t) -> 80/40 = 2 hrs on. Answer E.

SaquibHGMATWhiz · Answer

Solution: Let us assume the distance between fly and train be 36km We know that if the train remained stationary, the fly would reach the train in 4 hours, this means the speed of fly =\frac{distance}{time}=\frac{36}{4}=9 kmph We know that if the fly remained stationary, the train would hit it in 3 hours, this means the speed of train =\frac{36}{3}=12 kmph flytrain.png They both travel towards each other for 1 hour 20 mins i.e., 80 mins or \frac{80}{60}=\frac{4}{3} hrs In this \frac{4}{3} hrs: Fly traveled =speed imes time=9 imes \frac{4}{3}=12 km Train traveled =speed imes time=12 imes \frac{4}{3}=16 km Distance left between them =36-(12+16)=8 km, which needs to be covered by the train traveling at 12 kmph. flytrain2.png Time train will take to cover this 8 km =\frac{distance}{speed}=\frac{8}{12}=\frac{2}{3} hrs Total time of the journey =\frac{4}{3}+\frac{2}{3}=\frac{6}{3}=2 hrs Hence the right answer is Option E

darunp · Answer

Assuming distance between Fly & Train = x

Using speed =  \frac{distance}{time}

Speed of Fly =  \frac{x}{4}

Speed of Train =  \frac{x}{3}

Converting 1 hr 20 mins into hours =  \frac{4}{3}  hours

Distance covered by fly and train is  \frac{x}{3}  and  \frac{4x}{9} , respectively.

Remaining distance to be covered = x -  \frac{x}{3} -  \frac{4x}{9}  =  \frac{2x}{9}

Remaining time used by train =  \frac{2}{3}  hours

Total time =  \frac{2}{3}  +  \frac{4}{3}  = 2 hours

pappal · Answer

I tried this way, the time train hits fly from beginning should not be less than 4/3 hrs
all other options are less than this, so left automatically with 2 hrs.
so E

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A fly and a train are moving towards each other along a straight rail

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