Q1.

A swimming pool is filled with three

pipes with uniform flow. The 1^st two pipes operating simultaneously,fill the pool in the same time during which the pool is filled by 3^rd pipe alone. The second pipe fills the pool five hours faster than the first pipe and four hours slower than the third pipe.Find the time required by each pipe to fill the pool separately?

Q2.

A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed?

Ans.1By first pipe in x hours=1pool is filledBy 1st pipe in 1 hour=1/x pool is filledBy 2nd pipe in y hours = 1 poolBy 2nd pipe in 1 hour=1/y poolBy 3rd pipe in z hours=1poolBy 3rd pipe in 1 hour = 1/z pool1 hour work of 1st and 2nd=1/x+1/yA.T.S1/x+1/y=1/z (1)Also given y=x-5 (2)And y=z+4Or,z=y-4Z=(x-5)-4Z=x-9 (3)Put the value of y and z from eq(2) and eq(3) in eq(1)1/x+1/x-5=1/x-9X-5+x/x*2-5x=1/x-9(2x-5)(x-9)=x*2-5xX*2-18x+45=0x*2-15x-3x+45=0x(x-15)-3(x-15)=0(x-15)(x-3)=0(x-15)=0. Or. (X-3)=0X=15. X=3. It is not possible As if we take x=3 Time comes in -ve.Therefore x=15 hoursY=x-5=15-5=10 hoursZ=y-4=10-4=6 hours