Question

If the speed of the car is increased by 10 km/hr, it takes 18 minutes less to cover a distance of 36 km. Find the speed of the car.

Answer 1

Let the speed of the car be x

Time = distance/speed

Time taken to cover 36 km = 36/x hr

According to the question,

36/x - 36/(x+10) = 18/60

[36(x+10) - 36x]/x(x+10) = 3/10

(36x + 360 - 36x)/(x² + 10x) = 3/10

360 × 10 = 3(x² + 10x)

3x² + 30x = 3600

3x² + 30x - 3600= 0

3(x² + 10x - 1200)=0

x²+10x-1200 = 0

x² + 40x - 30x - 1200=0

x(x+40) - 30(x+ 40)= 0

(x-30)(x+40)=0

x-30 = 0 ; x+40 = 0

x = 30 ; x = -40

Here we do not consider x=-40 as speed (x) can not be negative.

So, x=30

Speed of the car = 30 km/hr

Hope it helps

★snehitha2 (brainly benefactor)★

Answer 2

Let initial speed of car = P km/h
and time taken by car = Q hours
we know,
time = distance/speed
use, this here,

initally :-
=========
time = distance/speed
Q = 36/P ------(1)

finally :-
========
time = distance/speed
Q - 18/60 = 36/(P + 10) ------(2)

put equation (1) Q value in equation (2)

36/P -3/10 = 36/(P + 10)

36/P -36/( P + 10) = 3/10

36{ P + 10 - P}/( P² + 10P ) = 3/10

12(10) = (P² + 10P)/10

P² + 10P -1200 = 0

P² + 40P -30P -1200 = 0

P(P + 40) -30(P + 40) = 0

( P -30)( P + 40) = 0

P = 30 and -40

but speed ≠ negative
so, P ≠ -40
hence, P = 30
so, initial speed of car = 30 km/h