A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.

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#### Solution

Let the original speed of the truck = s km/hr

New speed of the truck = (s + 20) km/hr

Time taken for 150 km + Time taken for 200 km = 5

`150/s+200/(s+20)=5`

`(150s+3000+200s)/(s(s+20))=5`

`(350s+3000)/(s(s+20))=5`

`(50(7s+60))/(s(s+20))=5`

`10(7s+ 60) =s(s+20)`

70s+600 = s^{2} + 20s

s^{2 }- 50s - 600 =0

s^{2 }- 60s -10s- 600 =0

(s - 10)(s - 60) = 0

s =10,60

s =10[Not possible]

First speed of the truck = 60 km/hr

Concept: Heights and Distances

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