Quadratic Equation Question. Please solve with all the steps. Thanks a lot in advance.

Question

A goods train leaves New Delhi at 5 p.m., followed by a passenger train, which leaves the station at 7 p.m. The passenger train travels 20km/hour faster than the goods train. The passenger train arrives at a station 1040 km away 2 hours 36 minutes before the goods train. Calculate their speeds.

Answer 1

Hi Suraj

Let X =  speed of goods train and Y = speed of passenger train

 Also as passenger train is faster Y = X + 20

Distance covered by each train is same = 1040 km

Let T1 = time taken by goodsr train and T2 time taken by passenger train for the same distance

 

Give T2 = T1 - ( 2+ 2.6)  as it starts 2 hr late and arrives 2.6 hr earlier than goods train) 2.6 hrs = 2 hr 36 min

So the equations are X= 1040/T1...... Eq 1 and Y = 1040/(T1 - 4.6)

or X+20 = 1040/ ( T1 - 4.6)......... Eq 2 

Solve these two eqations for X and T1 and the find Y and T2