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A car covers a distance of 1296 km in 16 hours. A truck covers 592 km in 8 hours. A bike covers 210 km in 5 hours. There are two roads X and Y of the same length. The bike and the truck are at either end of road X. The car has to travel on the road Y. The bike and the truck meet after 13 hours. Find the time(in hours) the car will take to cover the distance of road Y.
1. 14.32
2. 15.38
3. 19.21
4. 18.62

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Correct Answer - Option 4 : 18.62

Given:

A car covers a distance of 1296 km in 16 hours. A truck covers 592 km in 8 hours. A bike covers 210 km in 5 hours. There are two roads X and Y of the same length. The bike and the truck

are at either end of road X. The car has to travel on the road Y. The bike and the truck meet after 13 hours. 
 

Formula:

If the lengths of two trains are a and b,

Time taken to cross each other when travelling in same direction = (a + b)/(va - vb)

Time taken to cross each other when travelling in opposite direction = (a + b)/(va + vb)

where va and vb are the speeds of trains A and B respectively.

Calculation:

Speed of Car = 1296/16 = 81 km/hr

Speed of Truck = 592/8 = 74 km/hr

Speed of Bike = 592/5 = 42 km/hr

Let length of either road be l km.

⇒ l/(42 + 74) = 13

⇒ l = 116 (13) = 1508

Time car will take = l/speed of car = 1508/81 = 18.62

Car will take 18.62 hours.

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