Question

A truck covers a distance of 384 km at a certain speed. If the speed is decreased by 16 km/h. it will take 2 hours more to cover the

same distance. 75% of its original speed (in km/h) is:​

Answer 1

Answer:

75% of original speed is =48 km /hr

Step-by-step explanation:

Given,

Truck distance covered 384 km.

Speed of truck is =x km/hr

If speed of truck is decrease by 16 km/hr it will take 2 hours more to cover the same distance.

Find out the  75% of original speed of truck.

Solution,

New speed of truck is =(x-16)km/hr

$384/\left ( x-16 \right )-384/x=2$

$384\left ( 1/\left ( x-16 \right )-1/x \right )=2$

$384\left ( x-\left ( x-16 \right ) \right )/\left ( x\left ( x-16 \right ) \right )=2$

$384\left ( x-x+16 \right )=2\left ( x^{2}-16x \right )$

$192\times 16=x^{2}-16x$

$x^{2}-16x-3072=0$

$x^{2}-64x+48x-3072=0$

$x\left ( x-64 \right )+48\left ( x-64 \right )=0$

$\left ( x-64 \right )\left ( x+48 \right )=0$

$x-64=0$

$x=64$ km/hr

or

$x+48=0$

$x=-48$ km/hr  (Reject it because x=-48 km/hr never possible .Speed cannot be negative)

Calculate 75% of original speed

=$x\times 75%$%

=$x\times 3/4$

$64\times 3/4=48km/hr$