Question

(v) A train, travelling at a uniform speed for
480 km would take 48 minutes more to
travel that distance, if its speed was
reduced by 20 km/h. Find the original
speed of the train.
(HOTS)​

Answer 1

Answer:

Step-by-stIn this problem, two cases involving speed distance and time have been given . From the first case we get Speed v = 480/t

Or t = 480/v ……. equation one

Where v is the speed and t is time in first case and 1480 km is the total distance . We make the 2nd equation as follows :-

v - 8 = 480 / ( t + 3 )

Or t + 3 = 480 / v -8

Or t = ( 480 / v -8 ) - 3 ….. Equation two

Equating t of both equations one and two

v - 8 = 480 / ( 480/v +3 )

Or 3v squared - 24v- 3840 = 0

Or v squared - 8v - 1280 = 0

Solving the quadratic equation we get :-

v = 8 + ( square root of 64 +5120 or 5184 ) we get ( 8 + 72 ) / 2 or 40 . Ignoring negative root , we get 80/2 or 40 km / h . Therefore the train is travelling with a uniform speed of 40 km / h. We can check our answer in the following way .As the train is travellin gwith a uniform speed of 40 km / h , it takes a total time of 480/40 ie 12 h for the whole journey . The speed of the train had been reduced by 8 km / h . That it’s running at a reduced speed of 40 - 8 = 32 km / h . By running at this it will take 480 / 32 ie 15 hours which we see is 3 hours more than the time taken by the train to travel under first case . Hence our answer is correct.

ep explanation: