Two trains start traveling on same track from Mumbai and Pune at the constant speed of 45kmph and 30kmph in the direction of each other. Distance between Mumbai and Pune is 150 km. There is a fly sitting on the nose of one engine. The moment trains start, fly also starts flying in the direction of other train at 120kmph. It touches nose of approaching train and starts flying back till it touches nose of other train and repeats this exercise till trains collide and fly dies. How much distance fly will cover?
Variation: After half an hour, fly gets tired and hungry and takes a rest for 10 mins and feasts on crumbs of Vadapao fallen on Karjat platform for 10 mins and starts onward journey again. Her speed has now slowed down to 60 kmph after feasting. How much distance will it cover before trains collide?
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Total distance covered by fly is 130km
Speed of first train - 45 km/hr (Given)
Speed of second train - 30 km/Hr (Given)
Distance between Mumbai and Pune = 150 km (Given)
Let the time taken to collide be = t Hrs
Therefore,
= 45t + 30t = 150
= 75t = 150
= t = 150/75
= t = 2
Hence, after 2 Hrs the train will collide, which means that Fly will travel for 2 hrs at a speed 120 km/hr
Distance Covered by Fly = 2 × 120 = 240 km
Distance covered by fly in half hour = 120/2 = 60 km
Time taken for feast and Rest = 10 + 10 min = 20min (Given)
Remaining time to travel = 1 hr 10 min = 7/6 hrs
Speed = 60 km/Hr (Given)
Distance = 60 × 7/6
= 70 km
Therefore,
Total Distance travelled by fly
= 60 + 70
= 130 km
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