Question

A car left 30 minutes later than the scheduled time in order to reach its destination 150 km away in time it had to increase its speed by 25 km per hour from its usual speed find its usual speed.

Answer 1

Answer:- 75km/h

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Answer 2

The usual speed of car is 75 km/hr

Solution:

Let x be usual speed of the car in km/hr

Then,

Increased speed of car = (x + 25) km/hr

Distance = 150 km

A car left 30 minutes later than the scheduled time

$time = 30\ minutes = \frac{1}{2}\ hour$

$Time = \frac{distance}{speed}$

Then we can say,

$\frac{150}{x} - \frac{150}{x + 25} = \frac{1}{2}\\\\\frac{1}{x} - \frac{1}{x + 25} = \frac{1}{300}\\\\\frac{x + 25 - x }{x^2 + 25x} = \frac{1}{300}\\\\x^2 + 25x = 7500\\\\x^2 + 25x - 7500 = 0\\\\(x + 100)(x - 75) = 0$

x = - 100

Speed cannot be negative, so ignore -100

x = 75

Thus usual speed of car is 75 km/hr

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