Question

A train travels at a certain average speed for a distance of 54 km and

then travels a distance of 63 km at an average speed of 6 km/h more than

the first speed. If it takes 3 hours to complete the total journey, what is

its first speed ?

Answer 1

Answer:

First speed = 36 km/h = 10 m/s

Step-by-step explanation:

s1 = 54 km

v1 = v

t1 = s/v

   = 54/v

s2 = 63 km

v2 = v + 6

t2 = s/v

   = 63/(v + 6)

t1 + t2  = 3

54 / v + 63 / (v + 6) = 3

54(v + 6) + 63v = 3(v)(v + 6)

54v + 324 + 63v = 3v² + 18v

3v² - 99v - 324 = 0

v² - 33v - 108 = 0

v² - 36v + 3v - 108 = 0

v(v - 36) + 3(v - 36) = 0

(v - 36)(v - 3) = 0

Speed cannot be negative.

So, first speed = 36 km/h

                         = 10 m/s

Hope this helps! :)