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Question

A plane left 30minutes later than the scheduled time and in order to reach the destination, 1500kmaway in time. It has to increase the speed by 100km/hr from the usual seed. Find the usual speed?


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Solution

Given,
Distance covered by the plane =1500km
Let the usual speed be Skm/hr
Let the usual time taken be thr

we know,

Distance =Speed ×time

S×t=1500eq(1)

Now,

The plane left late and reached on time =30mins

=0.5hr
Time taken in this instance=(t-0.5)hr
Speed increased=100km/hr
Speed in this instance =(S+100)km/hr

(S+100)(t0.5)=1500eq(2)
Fromeq(1),t=1500S
On substituting t=1500Sineq(2)

We get,

S+1001500S-0.5=1500S+1001500-0.5SS=1500S+1001500-0.5S=1500S1500S-0.5S2+150000-50S=1500S0.5S2+50S-150000=0

On multiplying 2 the above equation. we get,

S2+100S-300000=0

S2+600S-500S-300000=0

S(S+600)-500(S+600)=0

(S+600)(S-500)=0

S=500km/hrorS=-600km/hr

Speed cannot be negative.
Hence, the speed of the plane=500km/hr


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