Question

A car travels from Singapore to Kuala Lumpur, covering 390 km in a period of x hours. A
slow train travels the same distance and it takes 4 hours more to reach the destination.
Find, in terms of x,
a) the average speed of the car in km/h
b) the average speed of the train in km/h
C) If the average speed of the train is 55 km/h faster than the train, form an equation in x
and show that it reduces to llx2 + 44x - 312 = 0.​

Answer 1

Answer:

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