Question

A car made a run of 390 km in 'x' hours. If
the speed had been 4 km/hour more, it would
have taken 2 hours less for the journey.
Find 'x'.

Answer 1

Let the actual speed be v km/hour

actual speed of run,v = distance/time = 390/x km/hour

if this speed is increased by 4 km/hour, time will be 2 hours less

i.e

(390/v) - [390/(v+4)] = 2 hours

⇒390[(v+4-v)/v(v+4)]= 2

⇒780 = v²+4v

⇒v²+4v - 780 =0

⇒v²+30v -26v -780=0

⇒v(v+30) -26(v+30)=0

⇒(v+30)(v-26)=0

so, v= 26 km/hours , neglecting negative value

so, time, x = 390/26 = 15 hours