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Doubt

amitabh covered a distance of 96km two hours faster than he had planned to.this he achieved by travelling 1km more every hour than he intented to cover every i hour 15 minutes.What was the speed at which amitabh travelled during the journey?
2.)how to solve the following equation if it is given d=st,d=(s+6)(t-4),d=(s-6)(t+10).here we have to find the distance.

Answer Explanation

1) let planned speed be xkm/hr

time to cover 96 km = T(96) = 96/x

distance covered in 1.25 hrs = 1.25x

new speed =(96)/{T(96)-2} = 96/(96/x-2)

new speed = 1.25x+1

both the new speeds should be equal

hence,

96/(96/x-2)=1.25x+1

25x^2-220x-960=0

x=12

New speed = 1.25*12+1 = 16 kph

2)d=st

eqn 2
d=(s+6)(t-4) =st
st -4s+6t-24=st
4s-6t= -24

2s-3t=-12

eqn3
d=(s-6)(t+10)=st
st+10s-6t-60=st
10s-6t=60
5s-3t=30

5*eqn2-2*eqn3

10s-15t-10s+6t=-60-60
-9t=-120
t=120/9
t=40/3

put t=40/3 in eqn 2 we get, s=14
d=st=560/3

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