Question

1. With the wind, an airplane travels 1120 km in seven hours. Against the wind, it takes eight

hours. Find the speed of the plane in still air and the velocity of the wind.

2. A passenger train leaves the train depot 2 hours after a freight train left the same depot. The

freight train is travelling 20 kmph slower than the passenger train. Find the speed of each

train, if the passenger train overtakes the freight train in three hours.

Answer 1

1-

Suppose the speed of plane in still air=u km/h

and speed of wind=v km/h

And also,we know that Speed=Distance / Time

Then according to question,

u+v=1120/7=160 --(i)

and u-v=1120/8=140--(ii)

Solving (i) and (ii),we get

u=150 km/h

and v=10 km/h

2-

Suppose speed of passenger train=xm/h

Speed of freight train=(x-20) m/h

Time taken by passenger train=3 hour

Then time taken by freight train=3+2=5hours

Now, Distance=Speed x Time

If the both trains are moving in same direction,

then 5(x - 20) = 3x

x = 50 (speed of passenger train)

and,

x – 20 = 30 (speed of freight train)